All language subtitles for 2024_Nature Machine Intelligence__Deep learning for predicting rate-induced tipping.en

all right okay so welcome back everyone

all right okay so welcome back everyone
so today it's my pleasure to welcome you

so today it's my pleasure to welcome you

so today it's my pleasure to welcome you
Hong who will be talking about deep

Hong who will be talking about deep

Hong who will be talking about deep
learning for uh critical transations

learning for uh critical transations

learning for uh critical transations
yeah thank you okay uh thank you and

yeah thank you okay uh thank you and

yeah thank you okay uh thank you and
thank you for your invitation and yeah

thank you for your invitation and yeah

thank you for your invitation and yeah
I'm very happy here uh to talk about our

I'm very happy here uh to talk about our

I'm very happy here uh to talk about our
recent work about uh uh using uh the

recent work about uh uh using uh the

recent work about uh uh using uh the
planning to predict R steing Points uh

planning to predict R steing Points uh

planning to predict R steing Points uh
yeah I'm a post doctor uh from uh Tech

yeah I'm a post doctor uh from uh Tech

yeah I'm a post doctor uh from uh Tech
Technical University of Munich and this

Technical University of Munich and this

Technical University of Munich and this
work is actually a co

work is actually a co

work is actually a co
cooporation uh study with my colleagues

cooporation uh study with my colleagues

cooporation uh study with my colleagues
Sebastian uh Peter and uh Nicholas

Sebastian uh Peter and uh Nicholas

Sebastian uh Peter and uh Nicholas
and

and

and
yeah uh firstly I want to give a very

yeah uh firstly I want to give a very

yeah uh firstly I want to give a very
brief uh intro introduction about the

brief uh intro introduction about the

brief uh intro introduction about the
Tipping points especially uh especially

Tipping points especially uh especially

Tipping points especially uh especially
in the

in the

in the
climate uh field yeah but as made maybe

climate uh field yeah but as made maybe

climate uh field yeah but as made maybe
most of uh the audience yeah you already

most of uh the audience yeah you already

most of uh the audience yeah you already
know uh a lot about uh tipping points um

know uh a lot about uh tipping points um

know uh a lot about uh tipping points um
but uh here I would start from the Earth

but uh here I would start from the Earth

but uh here I would start from the Earth
energ Balance model this is a very uh

energ Balance model this is a very uh

energ Balance model this is a very uh
very important also very famous uh basic

very important also very famous uh basic

very important also very famous uh basic
uh uh uh physical uh physical uh

uh uh uh physical uh physical uh

uh uh uh physical uh physical uh
conceptual model for the uh Earth

conceptual model for the uh Earth

conceptual model for the uh Earth
climate um understanding and also

climate um understanding and also

climate um understanding and also
sometimes for the simulation but if we

sometimes for the simulation but if we

sometimes for the simulation but if we
perform the uh simulation on this energ

perform the uh simulation on this energ

perform the uh simulation on this energ
balance model using different solar

balance model using different solar

balance model using different solar
radiative forcing this is a the

radiative forcing this is a the

radiative forcing this is a the
so-called control parameter Ro and if

so-called control parameter Ro and if

so-called control parameter Ro and if
way uh change uh uh increase or decrease

way uh change uh uh increase or decrease

way uh change uh uh increase or decrease
the control parameter and uh along the

the control parameter and uh along the

the control parameter and uh along the
time then we could

time then we could

time then we could
observe we can we will observe the

observe we can we will observe the

observe we can we will observe the
abrupt transition of the earth climate

abrupt transition of the earth climate

abrupt transition of the earth climate
from a from a warm warm climate St to a

from a from a warm warm climate St to a

from a from a warm warm climate St to a
cold warm climate state but it's also

cold warm climate state but it's also

cold warm climate state but it's also
possible uh just to tr Transit back from

possible uh just to tr Transit back from

possible uh just to tr Transit back from
uh back to the warm climate but uh just

uh back to the warm climate but uh just

uh back to the warm climate but uh just
along the different pathway uh but we

along the different pathway uh but we

along the different pathway uh but we
notice here the transition along the

notice here the transition along the

notice here the transition along the
time is uh is very uh is at just

time is uh is very uh is at just

time is uh is very uh is at just
suddenly transition uh not gradual

suddenly transition uh not gradual

suddenly transition uh not gradual
transition but here I would like firstly

transition but here I would like firstly

transition but here I would like firstly
I would like to use a very simple uh

I would like to use a very simple uh

I would like to use a very simple uh
example from the

example from the

example from the
realistic uh our realistic life to uh

realistic uh our realistic life to uh

realistic uh our realistic life to uh
explain the ab transition here I take

explain the ab transition here I take

explain the ab transition here I take
the I I just noticed some pictures for

the I I just noticed some pictures for

the I I just noticed some pictures for
the uh s greenw classier uh maybe over

the uh s greenw classier uh maybe over

the uh s greenw classier uh maybe over
uh 20 uh uh 250 50 years ago uh some uh

uh 20 uh uh 250 50 years ago uh some uh

uh 20 uh uh 250 50 years ago uh some uh
from some pictures over that time we

from some pictures over that time we

from some pictures over that time we
already we noticed there is a lot of

already we noticed there is a lot of

already we noticed there is a lot of
glassier during summer uh even during

glassier during summer uh even during

glassier during summer uh even during
summer uh over the glassier uh over

summer uh over the glassier uh over

summer uh over the glassier uh over
greart um Mountain Foods uh even until

greart um Mountain Foods uh even until

greart um Mountain Foods uh even until
20 years ago uh the mountain Foods uh

20 years ago uh the mountain Foods uh

20 years ago uh the mountain Foods uh
there is still a lot there was still a

there is still a lot there was still a

there is still a lot there was still a
lot of glassier and ice and Ice there

lot of glassier and ice and Ice there

lot of glassier and ice and Ice there
during summer but until most recent 10

during summer but until most recent 10

during summer but until most recent 10
years uh this glassier uh this ice over

years uh this glassier uh this ice over

years uh this glassier uh this ice over
the mountain food disappear Suddenly

the mountain food disappear Suddenly

the mountain food disappear Suddenly
It's very fast transition from the ice

It's very fast transition from the ice

It's very fast transition from the ice
to just to the board uh B B

to just to the board uh B B

to just to the board uh B B
rocks

rocks

rocks
but yeah uh and and the local people

but yeah uh and and the local people

but yeah uh and and the local people
also already noticed this uh this

also already noticed this uh this

also already noticed this uh this
phenomena and they really want to

phenomena and they really want to

phenomena and they really want to
protect uh this uh beautiful uh glassier

protect uh this uh beautiful uh glassier

protect uh this uh beautiful uh glassier
over the F Mountain food uh but this is

over the F Mountain food uh but this is

over the F Mountain food uh but this is
picture I take I uh from my camera this

picture I take I uh from my camera this

picture I take I uh from my camera this
uh the past uh September I noticed that

uh the past uh September I noticed that

uh the past uh September I noticed that
the local people really tried a lot uh

the local people really tried a lot uh

the local people really tried a lot uh
for example they built some damp they

for example they built some damp they

for example they built some damp they
they are trying to build some uh

they are trying to build some uh

they are trying to build some uh
construct some bad rocks for this glass

construct some bad rocks for this glass

construct some bad rocks for this glass
here and protect them but actually this

here and protect them but actually this

here and protect them but actually this
does not does not really work for for

does not does not really work for for

does not does not really work for for
the uh for pro uh avoid the shrink of

the uh for pro uh avoid the shrink of

the uh for pro uh avoid the shrink of
the glassier this means maybe in one

the glassier this means maybe in one

the glassier this means maybe in one
generation in our whole generation it's

generation in our whole generation it's

generation in our whole generation it's
really hard to recover the uh this glass

really hard to recover the uh this glass

really hard to recover the uh this glass
here this is also true a truth for the

here this is also true a truth for the

here this is also true a truth for the
Tipping points this also this could also

Tipping points this also this could also

Tipping points this also this could also
uh happen for a lot of climate sub

uh happen for a lot of climate sub

uh happen for a lot of climate sub
components uh uh components for example

components uh uh components for example

components uh uh components for example
like the uh Antarctic uh ocean

like the uh Antarctic uh ocean

like the uh Antarctic uh ocean
circulation also the uh Greenland SE

circulation also the uh Greenland SE

circulation also the uh Greenland SE
green L land SE ice also for some

green L land SE ice also for some

green L land SE ice also for some
vegetation uh like the Amazon uh Forest

vegetation uh like the Amazon uh Forest

vegetation uh like the Amazon uh Forest
this such a transition a bre transition

this such a transition a bre transition

this such a transition a bre transition
and E reversible transition would be uh

and E reversible transition would be uh

and E reversible transition would be uh
very possible for this uh nonlinear

very possible for this uh nonlinear

very possible for this uh nonlinear
system

system

system
so uh that a central Target of our uh

so uh that a central Target of our uh

so uh that a central Target of our uh
part of our climate people is to uh

part of our climate people is to uh

part of our climate people is to uh
anticipate the Tipping points and access

anticipate the Tipping points and access

anticipate the Tipping points and access
access the Tipping points risks uh on

access the Tipping points risks uh on

access the Tipping points risks uh on
behind the uh a specific climate syst

behind the uh a specific climate syst

behind the uh a specific climate syst
subsystem uh actually here uh I I would

subsystem uh actually here uh I I would

subsystem uh actually here uh I I would
uh we notice we could have s s methods

uh we notice we could have s s methods

uh we notice we could have s s methods
to uh anticipate tiing points from the

to uh anticipate tiing points from the

to uh anticipate tiing points from the
current condition but uh usually uh the

current condition but uh usually uh the

current condition but uh usually uh the
physical uh physical based researcher

physical uh physical based researcher

physical uh physical based researcher
would consider maybe uh we could uh find

would consider maybe uh we could uh find

would consider maybe uh we could uh find
find out the physical equations of a

find out the physical equations of a

find out the physical equations of a
specific um subsystem and then we could

specific um subsystem and then we could

specific um subsystem and then we could
recover the dynamical trajectory uh or

recover the dynamical trajectory uh or

recover the dynamical trajectory uh or
the face uh face base of the

the face uh face base of the

the face uh face base of the
um D the this dynamical system then we

um D the this dynamical system then we

um D the this dynamical system then we
can construct such a um verification

can construct such a um verification

can construct such a um verification
diagram for the for the interested

diagram for the for the interested

diagram for the for the interested
system then we can directly observe the

system then we can directly observe the

system then we can directly observe the
um the critical threshold for the tpping

um the critical threshold for the tpping

um the critical threshold for the tpping
points like like the uh here we can we

points like like the uh here we can we

points like like the uh here we can we
can find usually for a by stable State a

can find usually for a by stable State a

can find usually for a by stable State a
bable equ equili uh equilibriums States

bable equ equili uh equilibriums States

bable equ equili uh equilibriums States
we could find two t create uh critical

we could find two t create uh critical

we could find two t create uh critical
threshold for the forcing values uh to

threshold for the forcing values uh to

threshold for the forcing values uh to
then we can estimate uh if the system

then we can estimate uh if the system

then we can estimate uh if the system
will approach to the uh tipping points

will approach to the uh tipping points

will approach to the uh tipping points
but actually but usually this uh this

but actually but usually this uh this

but actually but usually this uh this
method does not really work well because

method does not really work well because

method does not really work well because
uh it's really hard to recover the whole

uh it's really hard to recover the whole

uh it's really hard to recover the whole
equations or dynamics of the realistic

equations or dynamics of the realistic

equations or dynamics of the realistic
system is especially like the um climate

system is especially like the um climate

system is especially like the um climate
system it's really hard so uh most

system it's really hard so uh most

system it's really hard so uh most
recent years uh scientists also find

recent years uh scientists also find

recent years uh scientists also find
some uh alternative way it's called the

some uh alternative way it's called the

some uh alternative way it's called the
critical slowing down maybe uh maybe you

critical slowing down maybe uh maybe you

critical slowing down maybe uh maybe you
already heard about it and that is we

already heard about it and that is we

already heard about it and that is we
can uh we can hold the we can have

can uh we can hold the we can have

can uh we can hold the we can have
really have the observational time

really have the observational time

really have the observational time
series of the

series of the

series of the
interested uh system for example here is

interested uh system for example here is

interested uh system for example here is
a

a

a
Greenland

Greenland

Greenland
uh uh say surface temperature uh from

uh uh say surface temperature uh from

uh uh say surface temperature uh from
the P climate records and uh here for

the P climate records and uh here for

the P climate records and uh here for
based on the time series um usually we

based on the time series um usually we

based on the time series um usually we
could we could make a linear assumption

could we could make a linear assumption

could we could make a linear assumption
when it's when the system is around its

when it's when the system is around its

when it's when the system is around its
equilibrium a fix point then we can we

equilibrium a fix point then we can we

equilibrium a fix point then we can we
can take a a a this uh uh this appro

can take a a a this uh uh this appro

can take a a a this uh uh this appro
approximation equation then um based on

approximation equation then um based on

approximation equation then um based on
the damping uh parameter Lambda we could

the damping uh parameter Lambda we could

the damping uh parameter Lambda we could
estimate if it's were uh under it were

estimate if it's were uh under it were

estimate if it's were uh under it were
if it were uh undergo at tipping points

if it were uh undergo at tipping points

if it were uh undergo at tipping points
the Lambda D dumping Lambda dumping

the Lambda D dumping Lambda dumping

the Lambda D dumping Lambda dumping
parameter Lambda when it's smaller than

parameter Lambda when it's smaller than

parameter Lambda when it's smaller than
zero it means the system will be stable

zero it means the system will be stable

zero it means the system will be stable
but if Lambda the increase to an

but if Lambda the increase to an

but if Lambda the increase to an
increase Anor to zero it will approach

increase Anor to zero it will approach

increase Anor to zero it will approach
to its critical threshold then when if

to its critical threshold then when if

to its critical threshold then when if
Lambda continue increase this also means

Lambda continue increase this also means

Lambda continue increase this also means
the external forcing will increase and

the external forcing will increase and

the external forcing will increase and
the system could be uh unstable will be

the system could be uh unstable will be

the system could be uh unstable will be
unstable and the Tipping points will

unstable and the Tipping points will

unstable and the Tipping points will
happens but usually for the Lambda

happens but usually for the Lambda

happens but usually for the Lambda
estimation we could make use of some

estimation we could make use of some

estimation we could make use of some
statist statistic Matrix like the uh

statist statistic Matrix like the uh

statist statistic Matrix like the uh
Auto coration of the time serious

Auto coration of the time serious

Auto coration of the time serious
segments and also usally the variance of

segments and also usally the variance of

segments and also usally the variance of
the time serious uh segments for example

the time serious uh segments for example

the time serious uh segments for example
here uh based on this Greenland

here uh based on this Greenland

here uh based on this Greenland
uh uh say surface temperature records uh

uh uh say surface temperature records uh

uh uh say surface temperature records uh
every time when there is abrupt

every time when there is abrupt

every time when there is abrupt
transition we can observe a uh increase

transition we can observe a uh increase

transition we can observe a uh increase
in the

in the

in the
autocorrelation and also the variance uh

autocorrelation and also the variance uh

autocorrelation and also the variance uh
of the time seral

of the time seral

of the time seral
this is a precursory signal uh of the uh

this is a precursory signal uh of the uh

this is a precursory signal uh of the uh
bation tipping

bation tipping

bation tipping
points uh of course recent years we also

points uh of course recent years we also

points uh of course recent years we also
have the third way uh from the data

have the third way uh from the data

have the third way uh from the data
science perspective uh based by using

science perspective uh based by using

science perspective uh based by using
the de planning Naro networks we can

the de planning Naro networks we can

the de planning Naro networks we can
also uh construct the early warning

also uh construct the early warning

also uh construct the early warning
signal of the Tipping points and here

signal of the Tipping points and here

signal of the Tipping points and here
based on the Thomas Barry's uh first

based on the Thomas Barry's uh first

based on the Thomas Barry's uh first
paper about about this direction uh

paper about about this direction uh

paper about about this direction uh
where we can find that uh critical

where we can find that uh critical

where we can find that uh critical
slowing down indicator and both critical

slowing down indicator and both critical

slowing down indicator and both critical
slowing down and the de planning

slowing down and the de planning

slowing down and the de planning
indicator can make prediction for the

indicator can make prediction for the

indicator can make prediction for the
bation Tipping points uh very well and

bation Tipping points uh very well and

bation Tipping points uh very well and
this is uh this is good for for our

this is uh this is good for for our

this is uh this is good for for our
tipping points and also climate climate

tipping points and also climate climate

tipping points and also climate climate
uh prediction uh communities

uh prediction uh communities

uh prediction uh communities
but uh uh most most recently um some

but uh uh most most recently um some

but uh uh most most recently um some
research some scientists just noticed

research some scientists just noticed

research some scientists just noticed
some different thing uh it's it's uh

some different thing uh it's it's uh

some different thing uh it's it's uh
it's based on a modeling research uh on

it's based on a modeling research uh on

it's based on a modeling research uh on
the ATL

the ATL

the ATL
Atlantic um o ocean circulation

Atlantic um o ocean circulation

Atlantic um o ocean circulation
simulation experiments usally we can

simulation experiments usally we can

simulation experiments usally we can
Define some safe uh space uh like when

Define some safe uh space uh like when

Define some safe uh space uh like when
we per from uh how can when we we will

we per from uh how can when we we will

we per from uh how can when we we will
know we have the we know we have the uh

know we have the we know we have the uh

know we have the we know we have the uh
global warming uh as a external forcing

global warming uh as a external forcing

global warming uh as a external forcing
to uh to the ocean circulation but when

to uh to the ocean circulation but when

to uh to the ocean circulation but when
the external forcing increase but U if

the external forcing increase but U if

the external forcing increase but U if
it's it has not reach uh a critical

it's it has not reach uh a critical

it's it has not reach uh a critical
threshold then this means our uh climb

threshold then this means our uh climb

threshold then this means our uh climb
system is safe is stable uh tipping

system is safe is stable uh tipping

system is safe is stable uh tipping
points will not happens and uh the

points will not happens and uh the

points will not happens and uh the
usually we can define a distin distinct

usually we can define a distin distinct

usually we can define a distin distinct
uh boundary for the safe operation uh

uh boundary for the safe operation uh

uh boundary for the safe operation uh
space between the safe the uh stable

space between the safe the uh stable

space between the safe the uh stable
climate and also and the and the bation

climate and also and the and the bation

climate and also and the and the bation
Tipping transation uh but something

Tipping transation uh but something

Tipping transation uh but something
different was noticed when uh yanas

different was noticed when uh yanas

different was noticed when uh yanas
Luman uh

Luman uh

Luman uh
research uh when they researched on the

research uh when they researched on the

research uh when they researched on the
uh aor simulation uh usually we can we

uh aor simulation uh usually we can we

uh aor simulation uh usually we can we
can construct such a bable equilibrium

can construct such a bable equilibrium

can construct such a bable equilibrium
State uh diagram and we can understand

State uh diagram and we can understand

State uh diagram and we can understand
it using the traditional bation theory

it using the traditional bation theory

it using the traditional bation theory
but um when uh when yanas uh and Peter

but um when uh when yanas uh and Peter

but um when uh when yanas uh and Peter
when they perform the different foring

when they perform the different foring

when they perform the different foring
uh rates uh on the AAR simulation that

uh rates uh on the AAR simulation that

uh rates uh on the AAR simulation that
is the fresh water forcing from the SE

is the fresh water forcing from the SE

is the fresh water forcing from the SE
Ice uh when they use different

Ice uh when they use different

Ice uh when they use different
increasing rate of the forcing um

increasing rate of the forcing um

increasing rate of the forcing um
specifically when they increase the

specifically when they increase the

specifically when they increase the
forcing rate like uh a very fast foring

forcing rate like uh a very fast foring

forcing rate like uh a very fast foring
rate uh then they notice the t uh the

rate uh then they notice the t uh the

rate uh then they notice the t uh the
clim the Amar uh state would uh reach

clim the Amar uh state would uh reach

clim the Amar uh state would uh reach
the uh tipping points much earlier than

the uh tipping points much earlier than

the uh tipping points much earlier than
avocation tipping points this is

avocation tipping points this is

avocation tipping points this is
uh this is out of out of blue and uh

uh this is out of out of blue and uh

uh this is out of out of blue and uh
yeah this is caused by the uh rting the

yeah this is caused by the uh rting the

yeah this is caused by the uh rting the
Tipping and uh this also could happen

Tipping and uh this also could happen

Tipping and uh this also could happen
for a lot of uh other nonlinear

for a lot of uh other nonlinear

for a lot of uh other nonlinear
system B basically uh around 10 years

system B basically uh around 10 years

system B basically uh around 10 years
ago uh um some studies already from the

ago uh um some studies already from the

ago uh um some studies already from the
mathematicians they already realized

mathematicians they already realized

mathematicians they already realized
maybe there will be three kinds of

maybe there will be three kinds of

maybe there will be three kinds of
tipping for the ninar systems uh

tipping for the ninar systems uh

tipping for the ninar systems uh
usually the the usual one we talk about

usually the the usual one we talk about

usually the the usual one we talk about
is the bation IND tipping points this

is the bation IND tipping points this

is the bation IND tipping points this
means under the uh under the slowing

means under the uh under the slowing

means under the uh under the slowing
changing uh external forcing the

changing uh external forcing the

changing uh external forcing the
attractor Bas of the uh system would

attractor Bas of the uh system would

attractor Bas of the uh system would
have a would change its shape and the uh

have a would change its shape and the uh

have a would change its shape and the uh
the equilibrium state would the the the

the equilibrium state would the the the

the equilibrium state would the the the
dynamical state would shift it would be

dynamical state would shift it would be

dynamical state would shift it would be
shifted also uh by just with external

shifted also uh by just with external

shifted also uh by just with external
forcing then it could change to another

forcing then it could change to another

forcing then it could change to another
state this is bation tipping points but

state this is bation tipping points but

state this is bation tipping points but
uh there is another another two two uh

uh there is another another two two uh

uh there is another another two two uh
kinds of tipping that is noise IND

kinds of tipping that is noise IND

kinds of tipping that is noise IND
tipping that is uh there's no very

tipping that is uh there's no very

tipping that is uh there's no very
strong external forcing but just some

strong external forcing but just some

strong external forcing but just some
noise perations or noise uh for things

noise perations or noise uh for things

noise perations or noise uh for things
but basically the uh the trct bre at

but basically the uh the trct bre at

but basically the uh the trct bre at
trct the Basin of the system could keep

trct the Basin of the system could keep

trct the Basin of the system could keep
its shape and uh and just because the uh

its shape and uh and just because the uh

its shape and uh and just because the uh
noise p uh noise forcing could drive the

noise p uh noise forcing could drive the

noise p uh noise forcing could drive the
uh system States from one equ

uh system States from one equ

uh system States from one equ
equilibrium state to another equilibrium

equilibrium state to another equilibrium

equilibrium state to another equilibrium
State this is the noising tipping but

State this is the noising tipping but

State this is the noising tipping but
for the rting Tipping I mentioned in

for the rting Tipping I mentioned in

for the rting Tipping I mentioned in
last slide it's uh it's uh caused by uh

last slide it's uh it's uh caused by uh

last slide it's uh it's uh caused by uh
the fast forcing specifically a fast

the fast forcing specifically a fast

the fast forcing specifically a fast
forcing that means the when the forcing

forcing that means the when the forcing

forcing that means the when the forcing
is very fast and uh comparably the

is very fast and uh comparably the

is very fast and uh comparably the
attractor Basin maybe it shape has not

attractor Basin maybe it shape has not

attractor Basin maybe it shape has not
been changed a lot but the equilibri but

been changed a lot but the equilibri but

been changed a lot but the equilibri but
the uh System state cannot uh attract

the uh System state cannot uh attract

the uh System state cannot uh attract
its original equilibrium State anymore

its original equilibrium State anymore

its original equilibrium State anymore
then it can just very easily shift uh

then it can just very easily shift uh

then it can just very easily shift uh
shift to another equilibrium state or

shift to another equilibrium state or

shift to another equilibrium state or
just collapse this is the r IND tipping

just collapse this is the r IND tipping

just collapse this is the r IND tipping
and they are the noise and R IND tipping

and they are the noise and R IND tipping

and they are the noise and R IND tipping
are just out of blue of the bation teing

are just out of blue of the bation teing

are just out of blue of the bation teing
diagram and uh what does this mean for

diagram and uh what does this mean for

diagram and uh what does this mean for
our climate system uh we know for the

our climate system uh we know for the

our climate system uh we know for the
future scenarios uh people always uh and

future scenarios uh people always uh and

future scenarios uh people always uh and
the society always worry about uh the um

the society always worry about uh the um

the society always worry about uh the um
global warming gas emissions and they

global warming gas emissions and they

global warming gas emissions and they
already designed different uh emission

already designed different uh emission

already designed different uh emission
Pathways trajectories Pathways this

Pathways trajectories Pathways this

Pathways trajectories Pathways this
means uh we could have various uh very

means uh we could have various uh very

means uh we could have various uh very
different forcing rates in the future

different forcing rates in the future

different forcing rates in the future
scenarios and but this means uh our

scenarios and but this means uh our

scenarios and but this means uh our
climate could have much more complex

climate could have much more complex

climate could have much more complex
tipping risks from the noise indu

tipping risks from the noise indu

tipping risks from the noise indu
tipping and R IND tipping uh diagram

tipping and R IND tipping uh diagram

tipping and R IND tipping uh diagram
maybe uh this means even where we don't

maybe uh this means even where we don't

maybe uh this means even where we don't
we have not reach a bation tipping

we have not reach a bation tipping

we have not reach a bation tipping
points a bation tipping points threshold

points a bation tipping points threshold

points a bation tipping points threshold
in the future scenario but our forcing

in the future scenario but our forcing

in the future scenario but our forcing
is very fast then uh it's also possible

is very fast then uh it's also possible

is very fast then uh it's also possible
for our climate lose its uh

stability uh

stability uh
so we really want to uh also make some

so we really want to uh also make some

so we really want to uh also make some
prediction for uh make some improvement

prediction for uh make some improvement

prediction for uh make some improvement
uh for the prediction of rting De

uh for the prediction of rting De

uh for the prediction of rting De
tipping this out of blue

tipping this out of blue

tipping this out of blue
tipping points and but but this is

tipping points and but but this is

tipping points and but but this is
really challenging because based on

really challenging because based on

really challenging because based on
recent most recent uh studies a series

recent most recent uh studies a series

recent most recent uh studies a series
of studies we already realized it's

of studies we already realized it's

of studies we already realized it's
really challenging firstly uh the

really challenging firstly uh the

really challenging firstly uh the
dynamical equation usually the dynamical

dynamical equation usually the dynamical

dynamical equation usually the dynamical
equation of our realistic system is

equation of our realistic system is

equation of our realistic system is
unknown and also uh we then we we can

unknown and also uh we then we we can

unknown and also uh we then we we can
really know the critical treshold holds

really know the critical treshold holds

really know the critical treshold holds
for uh for the Tipping rting tipping

for uh for the Tipping rting tipping

for uh for the Tipping rting tipping
secondly uh we Al uh we also already

secondly uh we Al uh we also already

secondly uh we Al uh we also already
know critical slowing down does not

know critical slowing down does not

know critical slowing down does not
necessarily work for uh uh for the noise

necessarily work for uh uh for the noise

necessarily work for uh uh for the noise
and rating the stepping because um

and rating the stepping because um

and rating the stepping because um
basically uh the critical slowing down

basically uh the critical slowing down

basically uh the critical slowing down
is based on the linear uh assumption

is based on the linear uh assumption

is based on the linear uh assumption
around the

around the

around the
equilibrium but in this Cas in the in

equilibrium but in this Cas in the in

equilibrium but in this Cas in the in
the in those tipping case this does not

the in those tipping case this does not

the in those tipping case this does not
necessarily

necessarily

necessarily
uh hold uh certainly and usually for the

uh hold uh certainly and usually for the

uh hold uh certainly and usually for the
realistic system the rate IND tipping

realistic system the rate IND tipping

realistic system the rate IND tipping
and noise IND tipping like the weather

and noise IND tipping like the weather

and noise IND tipping like the weather
perations also like some uh internal

perations also like some uh internal

perations also like some uh internal
varability of climate system it

varability of climate system it

varability of climate system it
could the usually happens together just

could the usually happens together just

could the usually happens together just
work in a concert to uh to our climate

work in a concert to uh to our climate

work in a concert to uh to our climate
system uh fourthly um it's also very

system uh fourthly um it's also very

system uh fourthly um it's also very
hard to General uh to uh get um get some

hard to General uh to uh get um get some

hard to General uh to uh get um get some
experience from the emble simulations of

experience from the emble simulations of

experience from the emble simulations of
climate models then make prediction on

climate models then make prediction on

climate models then make prediction on
some individual trajectories and in the

some individual trajectories and in the

some individual trajectories and in the
uh following slides I will explain this

uh following slides I will explain this

uh following slides I will explain this
two the uh the third one and the fourth

two the uh the third one and the fourth

two the uh the third one and the fourth
one uh first points in very

one uh first points in very

one uh first points in very
detail uh what what I mean the um the

detail uh what what I mean the um the

detail uh what what I mean the um the
rting de tiing here uh it's uh

rting de tiing here uh it's uh

rting de tiing here uh it's uh
uh it could be explained by this three

uh it could be explained by this three

uh it could be explained by this three
uh these three panels firstly when we

uh these three panels firstly when we

uh these three panels firstly when we
perform very slow uh slowly changing

perform very slow uh slowly changing

perform very slow uh slowly changing
forcing on the system perhaps the system

forcing on the system perhaps the system

forcing on the system perhaps the system
um the uh the dynamical state as a red

um the uh the dynamical state as a red

um the uh the dynamical state as a red
dots it will it it will always attract

dots it will it it will always attract

dots it will it it will always attract
it's uh equilibrium State fix point and

it's uh equilibrium State fix point and

it's uh equilibrium State fix point and
the Tipping points will not happens but

the Tipping points will not happens but

the Tipping points will not happens but
if way shift the attracted Basin of the

if way shift the attracted Basin of the

if way shift the attracted Basin of the
system very fast uh potentially the this

system very fast uh potentially the this

system very fast uh potentially the this
red bar it could not um really track its

red bar it could not um really track its

red bar it could not um really track its
original attractor Basin and just tip to

original attractor Basin and just tip to

original attractor Basin and just tip to
another uh another state this is

another uh another state this is

another uh another state this is
possible but in this two case

possible but in this two case

possible but in this two case
two cases uh there's there are no noise

two cases uh there's there are no noise

two cases uh there's there are no noise
there there are no noise

there there are no noise

there there are no noise
pations uh but if we uh cons in in

pations uh but if we uh cons in in

pations uh but if we uh cons in in
additional cons in addition consider uh

additional cons in addition consider uh

additional cons in addition consider uh
the noise pations like some weather uh

the noise pations like some weather uh

the noise pations like some weather uh
pations and some extreme extreme ex

pations and some extreme extreme ex

pations and some extreme extreme ex
internal viabilities in this case even

internal viabilities in this case even

internal viabilities in this case even
though the um uh the forcing shift rate

though the um uh the forcing shift rate

though the um uh the forcing shift rate
is not so fast but uh the r de tipping

is not so fast but uh the r de tipping

is not so fast but uh the r de tipping
can still happens this is what I mean

can still happens this is what I mean

can still happens this is what I mean
the um conert of the noise and the

the um conert of the noise and the

the um conert of the noise and the
rating D

rating D

rating D
tipping this could be very realistic for

tipping this could be very realistic for

tipping this could be very realistic for
um more closer to uh this could be

um more closer to uh this could be

um more closer to uh this could be
closer to our realistic cases like the

closer to our realistic cases like the

closer to our realistic cases like the
vegetation and also climate

vegetation and also climate

vegetation and also climate
systems and uh here we just take s uh uh

systems and uh here we just take s uh uh

systems and uh here we just take s uh uh
we just take three

we just take three

we just take three
uh typical uh dynamical system the sad

uh typical uh dynamical system the sad

uh typical uh dynamical system the sad
no and bolting and the compos boom uh

no and bolting and the compos boom uh

no and bolting and the compos boom uh
system and perform perform the fast

system and perform perform the fast

system and perform perform the fast
forcing uh external forcing on on this

forcing uh external forcing on on this

forcing uh external forcing on on this
three systems in uh spef uh respectively

three systems in uh spef uh respectively

three systems in uh spef uh respectively
and also perform at uh also add some

and also perform at uh also add some

and also perform at uh also add some
noise probations to them and uh then we

noise probations to them and uh then we

noise probations to them and uh then we
can get different simulations even for

can get different simulations even for

can get different simulations even for
example if we uh first have a look at

example if we uh first have a look at

example if we uh first have a look at
the S node system simulations we always

the S node system simulations we always

the S node system simulations we always
keep the same forcing the same forcing

keep the same forcing the same forcing

keep the same forcing the same forcing
profile and also the same forcing rate

profile and also the same forcing rate

profile and also the same forcing rate
forcing uh same uh forcing TR trajectory

forcing uh same uh forcing TR trajectory

forcing uh same uh forcing TR trajectory
time series um in this case we if we

time series um in this case we if we

time series um in this case we if we
have different white noise perturbations

have different white noise perturbations

have different white noise perturbations
on this system and the trajectory of the

on this system and the trajectory of the

on this system and the trajectory of the
system time series will be very

system time series will be very

system time series will be very
different

different

different
and here we notice some of them were

and here we notice some of them were

and here we notice some of them were
were TP but some of them were not and we

were TP but some of them were not and we

were TP but some of them were not and we
also make a statistic for the Tipping uh

also make a statistic for the Tipping uh

also make a statistic for the Tipping uh
tip time like the when this red lines

tip time like the when this red lines

tip time like the when this red lines
when this red time Ser

when this red time Ser

when this red time Ser
largely significant diverge from the uh

largely significant diverge from the uh

largely significant diverge from the uh
nontipping

nontipping

nontipping
category uh envelope then we can Define

category uh envelope then we can Define

category uh envelope then we can Define
The Tipping time and you you'll see here

The Tipping time and you you'll see here

The Tipping time and you you'll see here
the tiing time is uh the uncertainty of

the tiing time is uh the uncertainty of

the tiing time is uh the uncertainty of
the Tipping time is really large we

the Tipping time is really large we

the Tipping time is really large we
cannot we cannot really estimate uh

cannot we cannot really estimate uh

cannot we cannot really estimate uh
estimates The Tipping time simply from

estimates The Tipping time simply from

estimates The Tipping time simply from
the equations even though even though

the equations even though even though

the equations even though even though
now we already know the uh physical

now we already know the uh physical

now we already know the uh physical
equation mathematical uh equation of

equation mathematical uh equation of

equation mathematical uh equation of
this set no system but we can steer with

this set no system but we can steer with

this set no system but we can steer with
steer cannot really estimate the uh

steer cannot really estimate the uh

steer cannot really estimate the uh
forcing the thresholds of the tpping r

forcing the thresholds of the tpping r

forcing the thresholds of the tpping r
IND tpping and this uh this could this

IND tpping and this uh this could this

IND tpping and this uh this could this
would be similar uh for both for the

would be similar uh for both for the

would be similar uh for both for the
other two systems and of course this is

other two systems and of course this is

other two systems and of course this is
similar uh similar phenomenon uh are

similar uh similar phenomenon uh are

similar uh similar phenomenon uh are
already observed by Johannes and uh

already observed by Johannes and uh

already observed by Johannes and uh
Peter in the simul amok

simulations so uh here we we just want

simulations so uh here we we just want
to make some pred prediction for for

to make some pred prediction for for

to make some pred prediction for for
this tipping points we just know I

this tipping points we just know I

this tipping points we just know I
mentioned three main methods uh the

mentioned three main methods uh the

mentioned three main methods uh the
first methods it's yeah it does not work

first methods it's yeah it does not work

first methods it's yeah it does not work
here the F found are um threshold values

here the F found are um threshold values

here the F found are um threshold values
but it does not work here and uh then uh

but it does not work here and uh then uh

but it does not work here and uh then uh
we take the uh critical slowing down

we take the uh critical slowing down

we take the uh critical slowing down
indicators the auto

indicators the auto

indicators the auto
cation and and also the um variance of

cation and and also the um variance of

cation and and also the um variance of
the time serus here firstly if we uh uh

the time serus here firstly if we uh uh

the time serus here firstly if we uh uh
if we uh classify the uh simply Cate

if we uh classify the uh simply Cate

if we uh classify the uh simply Cate
make a category two categories for the

make a category two categories for the

make a category two categories for the
ring scenario and noning scenario for

ring scenario and noning scenario for

ring scenario and noning scenario for
our emble simulations time series or

our emble simulations time series or

our emble simulations time series or
samples then uh from the time serious

samples then uh from the time serious

samples then uh from the time serious
trajectory before the ring happens we

trajectory before the ring happens we

trajectory before the ring happens we
cannot uh we cannot find find out the uh

cannot uh we cannot find find out the uh

cannot uh we cannot find find out the uh
distinct the tping time Ser in visual

distinct the tping time Ser in visual

distinct the tping time Ser in visual
observation and then if we calculate the

observation and then if we calculate the

observation and then if we calculate the
uh alation and the variance of the two

uh alation and the variance of the two

uh alation and the variance of the two
categories then we will find there there

categories then we will find there there

categories then we will find there there
is no diff almost no vual difference for

is no diff almost no vual difference for

is no diff almost no vual difference for
the r tping and the nontipping

the r tping and the nontipping

the r tping and the nontipping
categories uh but of course uh for the

categories uh but of course uh for the

categories uh but of course uh for the
uh deping methods uh we can distinguish

uh deping methods uh we can distinguish

uh deping methods uh we can distinguish
them very well but I will introduce uh

them very well but I will introduce uh

them very well but I will introduce uh
the Third indicator

the Third indicator

the Third indicator
later and yeah but still we we still

later and yeah but still we we still

later and yeah but still we we still
believe maybe we we can find some find

believe maybe we we can find some find

believe maybe we we can find some find
out some uh uh find out some evidence of

out some uh uh find out some evidence of

out some uh uh find out some evidence of
the potential PR predictability of the

the potential PR predictability of the

the potential PR predictability of the
ring from the raw data that means and

ring from the raw data that means and

ring from the raw data that means and
here we have the time serious or we

here we have the time serious or we

here we have the time serious or we
already have the time series of tpping

already have the time series of tpping

already have the time series of tpping
and non- tipping categories then uh

and non- tipping categories then uh

and non- tipping categories then uh
focus on the specific uh leading time uh

focus on the specific uh leading time uh

focus on the specific uh leading time uh
before the Tipping happens for example

before the Tipping happens for example

before the Tipping happens for example
here uh if if we take the 100 time steps

here uh if if we take the 100 time steps

here uh if if we take the 100 time steps
before the Tipping and make a make a

before the Tipping and make a make a

before the Tipping and make a make a
slides for the uh for the the two

slides for the uh for the the two

slides for the uh for the the two
envelopes then we can get a uh PDF and a

envelopes then we can get a uh PDF and a

envelopes then we can get a uh PDF and a
probability distribution of these two

probability distribution of these two

probability distribution of these two
categories and we can visually we can

categories and we can visually we can

categories and we can visually we can
really observe some difference between

really observe some difference between

really observe some difference between
these two uh categories but uh uh but in

these two uh categories but uh uh but in

these two uh categories but uh uh but in
um practice if we really want to make

um practice if we really want to make

um practice if we really want to make
prediction based on this uh based on the

prediction based on this uh based on the

prediction based on this uh based on the
diff visual difference from the uh from

diff visual difference from the uh from

diff visual difference from the uh from
the probability distribution then it

the probability distribution then it

the probability distribution then it
will uh will make you uh disappointed

will uh will make you uh disappointed

will uh will make you uh disappointed
because but but I will introduce the

because but but I will introduce the

because but but I will introduce the
prediction results based on this uh

prediction results based on this uh

prediction results based on this uh
probability distribution later but yeah

probability distribution later but yeah

probability distribution later but yeah
I can I can tell here it does not work

I can I can tell here it does not work

I can I can tell here it does not work
well and also we we observe some we also

well and also we we observe some we also

well and also we we observe some we also
have a look at the uh distribution

have a look at the uh distribution

have a look at the uh distribution
difference uh on the based on the autoc

difference uh on the based on the autoc

difference uh on the based on the autoc
coration indicator and also the variance

coration indicator and also the variance

coration indicator and also the variance
uh indicator and indeed we can observe

uh indicator and indeed we can observe

uh indicator and indeed we can observe
some difference in the uh

some difference in the uh

some difference in the uh
uh in in the PDF but uh uh but still it

uh in in the PDF but uh uh but still it

uh in in the PDF but uh uh but still it
cannot really help us to make prediction

cannot really help us to make prediction

cannot really help us to make prediction
for a uh individual tra trajectories uh

for a uh individual tra trajectories uh

for a uh individual tra trajectories uh
that means basically we can if we

that means basically we can if we

that means basically we can if we
observe the and we already know the um

observe the and we already know the um

observe the and we already know the um
envelopes of the Tipping and nontipping

envelopes of the Tipping and nontipping

envelopes of the Tipping and nontipping
trajectory but um hopefully for

trajectory but um hopefully for

trajectory but um hopefully for
individual trajectory time series we we

individual trajectory time series we we

individual trajectory time series we we
can also make the prediction but

can also make the prediction but

can also make the prediction but
uh yeah this is what we want uh just um

uh yeah this is what we want uh just um

uh yeah this is what we want uh just um
get some experience from the emble

get some experience from the emble

get some experience from the emble
simulations and then make the prediction

simulations and then make the prediction

simulations and then make the prediction
for a specific TR uh time series uh this

for a specific TR uh time series uh this

for a specific TR uh time series uh this
is also usually what we did for the uh

is also usually what we did for the uh

is also usually what we did for the uh
climate in the climate uh

climate in the climate uh

climate in the climate uh
studies uh so here uh let's uh let's

studies uh so here uh let's uh let's

studies uh so here uh let's uh let's
move to to the uh the third indicator

move to to the uh the third indicator

move to to the uh the third indicator
the third prediction method uh the deing

the third prediction method uh the deing

the third prediction method uh the deing
method here uh we we just take the time

method here uh we we just take the time

method here uh we we just take the time
serious from The Tipping and nontipping

serious from The Tipping and nontipping

serious from The Tipping and nontipping
categories and then for example here we

categories and then for example here we

categories and then for example here we
uh just pick uh pick up a time serious

uh just pick uh pick up a time serious

uh just pick uh pick up a time serious
segment uh just with a with a certain

segment uh just with a with a certain

segment uh just with a with a certain
Focus lead time to the tiing points then

Focus lead time to the tiing points then

Focus lead time to the tiing points then
fed it fed them into the Neal networks

fed it fed them into the Neal networks

fed it fed them into the Neal networks
here uh and then hopefully we uh we hope

here uh and then hopefully we uh we hope

here uh and then hopefully we uh we hope
the expect the uh neon networks can give

the expect the uh neon networks can give

the expect the uh neon networks can give
us uh can give us the a classification

us uh can give us the a classification

us uh can give us the a classification
results it's basically the ring

results it's basically the ring

results it's basically the ring
probability and the nontipping

probability and the nontipping

probability and the nontipping
probability of this time series uh here

probability of this time series uh here

probability of this time series uh here
are the Naro Network for the Naro

are the Naro Network for the Naro

are the Naro Network for the Naro
Network architecture we take we took a

Network architecture we take we took a

Network architecture we take we took a
very simple architecture based on the

very simple architecture based on the

very simple architecture based on the
well known uh s architecture uh Neal

well known uh s architecture uh Neal

well known uh s architecture uh Neal
Network here we take two S Neal Network

Network here we take two S Neal Network

Network here we take two S Neal Network
and uh then uh and and then uh combine

and uh then uh and and then uh combine

and uh then uh and and then uh combine
them with a fully connected uh Naro

them with a fully connected uh Naro

them with a fully connected uh Naro
Network this is very simple because uh

Network this is very simple because uh

Network this is very simple because uh
we uh we want to yeah we expect if the

we uh we want to yeah we expect if the

we uh we want to yeah we expect if the
very s very simple Naro Network

very s very simple Naro Network

very s very simple Naro Network
architectures can work for the T WR

architectures can work for the T WR

architectures can work for the T WR
those tipping prediction then hopefully

those tipping prediction then hopefully

those tipping prediction then hopefully
the more much more complicated

the more much more complicated

the more much more complicated
architecture will also works um so here

architecture will also works um so here

architecture will also works um so here
let's say the uh prediction uh results

let's say the uh prediction uh results

let's say the uh prediction uh results
here uh firstly let's have a look at the

here uh firstly let's have a look at the

here uh firstly let's have a look at the
S node system time Ser here uh I only

S node system time Ser here uh I only

S node system time Ser here uh I only
present two time Ser of this from this

present two time Ser of this from this

present two time Ser of this from this
system and here the the red one one is

system and here the the red one one is

system and here the the red one one is
for the Tipping time serus blue one is

for the Tipping time serus blue one is

for the Tipping time serus blue one is
the nontipping case and here if um by

the nontipping case and here if um by

the nontipping case and here if um by
fit them into the trended uh Naro

fit them into the trended uh Naro

fit them into the trended uh Naro
networks then the Naro Network could

networks then the Naro Network could

networks then the Naro Network could
give uh provide as uh the indicator ex

give uh provide as uh the indicator ex

give uh provide as uh the indicator ex
exactly the um RTP probability of this

exactly the um RTP probability of this

exactly the um RTP probability of this
time seral at different forecast lead

time seral at different forecast lead

time seral at different forecast lead
time and when this when the time is

time and when this when the time is

time and when this when the time is
approach to the uh tipping uh tipping

approach to the uh tipping uh tipping

approach to the uh tipping uh tipping
points then for the non- Tipping case

points then for the non- Tipping case

points then for the non- Tipping case
it's tipping probability where

it's tipping probability where

it's tipping probability where
continuous increase until 100% but for

continuous increase until 100% but for

continuous increase until 100% but for
the non- Tipping case uh its predict

the non- Tipping case uh its predict

the non- Tipping case uh its predict
probability tipping probability will

probability tipping probability will

probability tipping probability will
decree continuously uh decrease and they

decree continuously uh decrease and they

decree continuously uh decrease and they
just this two this indicators for this

just this two this indicators for this

just this two this indicators for this
two times Ser just develop alone uh two

two times Ser just develop alone uh two

two times Ser just develop alone uh two
opposite directions but for the uh autoc

opposite directions but for the uh autoc

opposite directions but for the uh autoc
colation and the uh Rance

colation and the uh Rance

colation and the uh Rance
indicators yeah they both give the

indicators yeah they both give the

indicators yeah they both give the
increase uh increase signal but we

increase uh increase signal but we

increase uh increase signal but we
cannot really yeah infer if there will

cannot really yeah infer if there will

cannot really yeah infer if there will
be a tipping points for uh for the blue

be a tipping points for uh for the blue

be a tipping points for uh for the blue
or red uh time series before the Tipping

or red uh time series before the Tipping

or red uh time series before the Tipping
happens uh this similar thing also

happens uh this similar thing also

happens uh this similar thing also
similar phenomena conclusion can be also

similar phenomena conclusion can be also

similar phenomena conclusion can be also
find from the uh boting system and

find from the uh boting system and

find from the uh boting system and
compost boom uh

compost boom uh

compost boom uh
system yeah here talk a bit about the

system yeah here talk a bit about the

system yeah here talk a bit about the
training data that's used for the model

training data that's used for the model

training data that's used for the model
what kind of training data was used yeah

what kind of training data was used yeah

what kind of training data was used yeah
and the training data basically it's uh

and the training data basically it's uh

and the training data basically it's uh
it's here uh if we have a look at time

it's here uh if we have a look at time

it's here uh if we have a look at time
series in this slide uh the first panel

series in this slide uh the first panel

series in this slide uh the first panel
here uh the uh wait yeah

here uh the uh wait yeah

here uh the uh wait yeah
[Music]

[Music]

[Music]
and this envelope is is made from the a

and this envelope is is made from the a

and this envelope is is made from the a
lot of time serious is emble simulations

lot of time serious is emble simulations

lot of time serious is emble simulations
this means uh here we perform the same

this means uh here we perform the same

this means uh here we perform the same
external forcing on the same system but

external forcing on the same system but

external forcing on the same system but
using different White Noise

using different White Noise

using different White Noise
realizations then we can get

realizations then we can get

realizations then we can get
different uh we can that get different

different uh we can that get different

different uh we can that get different
simulations this is just like the uh

simulations this is just like the uh

simulations this is just like the uh
climate also like the climate

climate also like the climate

climate also like the climate
simulations we we give the different uh

simulations we we give the different uh

simulations we we give the different uh
pations then we can get different uh

pations then we can get different uh

pations then we can get different uh
trajectories this is then yeah our data

trajectories this is then yeah our data

trajectories this is then yeah our data
sets uh source and the the the training

sets uh source and the the the training

sets uh source and the the the training
training set is uh basically we only

training set is uh basically we only

training set is uh basically we only
have two this is a uh classifier Naro

have two this is a uh classifier Naro

have two this is a uh classifier Naro
network is a classifier uh we only fed

network is a classifier uh we only fed

network is a classifier uh we only fed
two kinds of data one is tipping data n

two kinds of data one is tipping data n

two kinds of data one is tipping data n
uh second is nontipping uh nontipping

uh second is nontipping uh nontipping

uh second is nontipping uh nontipping
data and uh and we also labor labor them

data and uh and we also labor labor them

data and uh and we also labor labor them
as zero and one respectively then we can

as zero and one respectively then we can

as zero and one respectively then we can
get the uh tipping probab the uh

get the uh tipping probab the uh

get the uh tipping probab the uh
classifier probability for these two

classifier probability for these two

classifier probability for these two
category two

category two

category two
classifications yeah I hope this is

classifications yeah I hope this is

classifications yeah I hope this is
clear to you yeah

clear to you yeah

clear to you yeah
so it's climate simulation data that's

so it's climate simulation data that's

so it's climate simulation data that's
used for for training um ENT so

used for for training um ENT so

used for for training um ENT so
essentially this model is capturing the

essentially this model is capturing the

essentially this model is capturing the
the way in which those climate models uh

the way in which those climate models uh

the way in which those climate models uh
identify the r typing

identify the r typing

identify the r typing
yes okay yeah thanks okay yeah you're

yes okay yeah thanks okay yeah you're

yes okay yeah thanks okay yeah you're
welome and but yeah of course here in

welome and but yeah of course here in

welome and but yeah of course here in
current stage uh the model which

current stage uh the model which

current stage uh the model which
actually train three kinds of model um

actually train three kinds of model um

actually train three kinds of model um
each kind of model specifically for a

each kind of model specifically for a

each kind of model specifically for a
specific a certain system for example

specific a certain system for example

specific a certain system for example
for S no system which and the Neo

for S no system which and the Neo

for S no system which and the Neo
networks but for the boting system we

networks but for the boting system we

networks but for the boting system we
will retrain a we will train a new uh

will retrain a we will train a new uh

will retrain a we will train a new uh
deing model for its prediction and uh

deing model for its prediction and uh

deing model for its prediction and uh
but but in in the uh last slides uh in

but but in in the uh last slides uh in

but but in in the uh last slides uh in
the later uh following slides I will

the later uh following slides I will

the later uh following slides I will
also present uh the uh inter model

also present uh the uh inter model

also present uh the uh inter model
interstem

interstem

interstem
prediction uh but here it's we can OB

prediction uh but here it's we can OB

prediction uh but here it's we can OB
everything is clear and we can

everything is clear and we can

everything is clear and we can
understand the understand the system and

understand the understand the system and

understand the understand the system and
de planing very Behavior Uh better in

de planing very Behavior Uh better in

de planing very Behavior Uh better in
this way yeah uh here I yeah I would

this way yeah uh here I yeah I would

this way yeah uh here I yeah I would
yeah make a simple make some simple U

yeah make a simple make some simple U

yeah make a simple make some simple U
comparation between the S tipping uh the

comparation between the S tipping uh the

comparation between the S tipping uh the
between the say critical slowing down

between the say critical slowing down

between the say critical slowing down
indicator and say uh de planning

indicator and say uh de planning

indicator and say uh de planning
indicator comparation here we we notice

indicator comparation here we we notice

indicator comparation here we we notice
for the auto coralation when we perform

for the auto coralation when we perform

for the auto coralation when we perform
the uh prediction on all the uh time

the uh prediction on all the uh time

the uh prediction on all the uh time
serial samples then we can observe the

serial samples then we can observe the

serial samples then we can observe the
uh for the uh for the uh deing indicator

uh for the uh for the uh deing indicator

uh for the uh for the uh deing indicator
uh they can it can always help uh it can

uh they can it can always help uh it can

uh they can it can always help uh it can
always help us distinguish The Tipping

always help us distinguish The Tipping

always help us distinguish The Tipping
and tipping and nontipping

and tipping and nontipping

and tipping and nontipping
uh

uh

uh
category with a considerable uh forecast

category with a considerable uh forecast

category with a considerable uh forecast
lead

lead

lead
time of course here uh we we also make a

time of course here uh we we also make a

time of course here uh we we also make a
estimate uh evaluation for the um uh for

estimate uh evaluation for the um uh for

estimate uh evaluation for the um uh for
the de planning prediction actually it's

the de planning prediction actually it's

the de planning prediction actually it's
it's a classif it's just a classifier uh

it's a classif it's just a classifier uh

it's a classif it's just a classifier uh
for the Tipping and nontipping uh but

for the Tipping and nontipping uh but

for the Tipping and nontipping uh but
let's firstly have a look at the bottom

let's firstly have a look at the bottom

let's firstly have a look at the bottom
panels bottom panels means the a

panels bottom panels means the a

panels bottom panels means the a
different col the blue and red colors

different col the blue and red colors

different col the blue and red colors
represents the uh testing data set and

represents the uh testing data set and

represents the uh testing data set and
the training data set uh

the training data set uh

the training data set uh
uh overall uh the the training and the

uh overall uh the the training and the

uh overall uh the the training and the
testing

testing

testing
accuracy uh curve are over almost

accuracy uh curve are over almost

accuracy uh curve are over almost
overlapped this means our model is

overlapped this means our model is

overlapped this means our model is
robust and the and and and

robust and the and and and

robust and the and and and
we don't need to worry about the

we don't need to worry about the

we don't need to worry about the
overfitting problem but of course we

overfitting problem but of course we

overfitting problem but of course we
also perform the cross validation uh a

also perform the cross validation uh a

also perform the cross validation uh a
lot of a com

lot of a com

lot of a com
extensive uh evaluation on to check if

extensive uh evaluation on to check if

extensive uh evaluation on to check if
there is any

there is any

there is any
um overfitting uh issue for the model

um overfitting uh issue for the model

um overfitting uh issue for the model
but uh the results also show the

but uh the results also show the

but uh the results also show the
overfitting almost very weak here and

overfitting almost very weak here and

overfitting almost very weak here and
and also where uh in the very beginning

and also where uh in the very beginning

and also where uh in the very beginning
of our when we have a look at the time

of our when we have a look at the time

of our when we have a look at the time
serious T tipping and nontipping time

serious T tipping and nontipping time

serious T tipping and nontipping time
serious I mentioned we can uh actually

serious I mentioned we can uh actually

serious I mentioned we can uh actually
make a very simple prediction based on

make a very simple prediction based on

make a very simple prediction based on
the uh probability distribution of the

the uh probability distribution of the

the uh probability distribution of the
tpping and noning and uh yeah we write

tpping and noning and uh yeah we write

tpping and noning and uh yeah we write
uh we uh create some very simple

uh we uh create some very simple

uh we uh create some very simple
algorithm to realize the probability uh

algorithm to realize the probability uh

algorithm to realize the probability uh
distribution based prediction

distribution based prediction

distribution based prediction
uh method and uh and we compare it with

uh method and uh and we compare it with

uh method and uh and we compare it with
our deing indicator here and same uh

our deing indicator here and same uh

our deing indicator here and same uh
deing indicator uh have better um

deing indicator uh have better um

deing indicator uh have better um
accuracy uh than the uh than the visual

accuracy uh than the uh than the visual

accuracy uh than the uh than the visual
visual observation on the um probability

visual observation on the um probability

visual observation on the um probability
distribution yeah and uh in the

distribution yeah and uh in the

distribution yeah and uh in the
following I would like to uh pres uh

following I would like to uh pres uh

following I would like to uh pres uh
introduce some very interesting

introduce some very interesting

introduce some very interesting
phenomena based on our analyze on our uh

phenomena based on our analyze on our uh

phenomena based on our analyze on our uh
trended def uh deing model uh firstly we

trended def uh deing model uh firstly we

trended def uh deing model uh firstly we
uh just uh we want to discuss about out

uh just uh we want to discuss about out

uh just uh we want to discuss about out
out of sample prediction of dep planning

out of sample prediction of dep planning

out of sample prediction of dep planning
uh because this is this is very

uh because this is this is very

uh because this is this is very
important um for uh for the data science

important um for uh for the data science

important um for uh for the data science
uh usually we train our model on a

uh usually we train our model on a

uh usually we train our model on a
specific uh some specific data sets but

specific uh some specific data sets but

specific uh some specific data sets but
but

but

but
afterwards uh when we met some new data

afterwards uh when we met some new data

afterwards uh when we met some new data
set data resource uh our

set data resource uh our

set data resource uh our
model uh it it would be some uh it would

model uh it it would be some uh it would

model uh it it would be some uh it would
be dangerous for a model to make some

be dangerous for a model to make some

be dangerous for a model to make some
some U make prediction on some unseen a

some U make prediction on some unseen a

some U make prediction on some unseen a
previously unseen data resource uh so

previously unseen data resource uh so

previously unseen data resource uh so
here we want to discuss about this point

here we want to discuss about this point

here we want to discuss about this point
uh firstly we test our model for the out

uh firstly we test our model for the out

uh firstly we test our model for the out
of sample foring rates prediction uh uh

of sample foring rates prediction uh uh

of sample foring rates prediction uh uh
prediction uh that is just now I

prediction uh that is just now I

prediction uh that is just now I
mentioned uh the model the model I me

mentioned uh the model the model I me

mentioned uh the model the model I me
trended model I mentioned just now is

trended model I mentioned just now is

trended model I mentioned just now is
all uh is trended based on a fixed

all uh is trended based on a fixed

all uh is trended based on a fixed
forcing rate for example here uh

forcing rate for example here uh

forcing rate for example here uh
actually for the set node system

actually for the set node system

actually for the set node system
basically we can design different

basically we can design different

basically we can design different
forcing forcing rates for it but when we

forcing forcing rates for it but when we

forcing forcing rates for it but when we
train our deing model uh we always use a

train our deing model uh we always use a

train our deing model uh we always use a
fixed forcing rates

fixed forcing rates

fixed forcing rates
the foring rate is just the diff uh the

the foring rate is just the diff uh the

the foring rate is just the diff uh the
um it can be controlled uh controlled by

um it can be controlled uh controlled by

um it can be controlled uh controlled by
the parameter Lambda in the S node

the parameter Lambda in the S node

the parameter Lambda in the S node
system and uh yeah here we take the only

system and uh yeah here we take the only

system and uh yeah here we take the only
take a fixed forcing rate it's

take a fixed forcing rate it's

take a fixed forcing rate it's
1.25 like like this dash line

1.25 like like this dash line

1.25 like like this dash line
sh um uh when we TR trained on after we

sh um uh when we TR trained on after we

sh um uh when we TR trained on after we
trained our model we have fixed

trained our model we have fixed

trained our model we have fixed
everything uh unchanged and just let

everything uh unchanged and just let

everything uh unchanged and just let
uh uh just let's

uh uh just let's

uh uh just let's
uh just use the trended deing model to

uh just use the trended deing model to

uh just use the trended deing model to
make prediction for other uh time serus

make prediction for other uh time serus

make prediction for other uh time serus
uh the other time serus are generated

uh the other time serus are generated

uh the other time serus are generated
from the different uh foring rates and

from the different uh foring rates and

from the different uh foring rates and
these forcing rates are unseen during

these forcing rates are unseen during

these forcing rates are unseen during
the training Pro uh training phase and

the training Pro uh training phase and

the training Pro uh training phase and
here it seems uh it's still work for

here it seems uh it's still work for

here it seems uh it's still work for
other foring rate uh but and uh it seems

other foring rate uh but and uh it seems

other foring rate uh but and uh it seems
it could work for the out of sample

it could work for the out of sample

it could work for the out of sample
forcing rate so in the following way we

forcing rate so in the following way we

forcing rate so in the following way we
further uh train a new uh deing model

further uh train a new uh deing model

further uh train a new uh deing model
for the set node system prediction here

for the set node system prediction here

for the set node system prediction here
we just take another fixed forcing rate

we just take another fixed forcing rate

we just take another fixed forcing rate
like the uh panel d uh in the panel D we

like the uh panel d uh in the panel D we

like the uh panel d uh in the panel D we
use another forcing rate and generates

use another forcing rate and generates

use another forcing rate and generates
the data and the Train the deping model

the data and the Train the deping model

the data and the Train the deping model
then um your the trended model predicts

then um your the trended model predicts

then um your the trended model predicts
the unse forcing rates on for other time

the unse forcing rates on for other time

the unse forcing rates on for other time
series like here panel D and here if we

series like here panel D and here if we

series like here panel D and here if we
compare panel a and panel d uh the deing

compare panel a and panel d uh the deing

compare panel a and panel d uh the deing
model are trended on different forcing

model are trended on different forcing

model are trended on different forcing
rate but uh the accuracy pattern uh are

rate but uh the accuracy pattern uh are

rate but uh the accuracy pattern uh are
very similar for this uh the two uh uh

very similar for this uh the two uh uh

very similar for this uh the two uh uh
trended trended models and uh

trended trended models and uh

trended trended models and uh
uh for the pan in the panel G uh basic

uh for the pan in the panel G uh basic

uh for the pan in the panel G uh basic
actually this is we did a additional

actually this is we did a additional

actually this is we did a additional
experiment where just fed uh fed uh fed

experiment where just fed uh fed uh fed

experiment where just fed uh fed uh fed
all the forcing rate time seral into the

all the forcing rate time seral into the

all the forcing rate time seral into the
uh deing model then in this case uh

uh deing model then in this case uh

uh deing model then in this case uh
there will be no unseen previous

there will be no unseen previous

there will be no unseen previous
previously unseen foring rates for the

previously unseen foring rates for the

previously unseen foring rates for the
deing model then we compare the

deing model then we compare the

deing model then we compare the
prediction accurate pattern uh from

prediction accurate pattern uh from

prediction accurate pattern uh from
panel a d g and they looks uh very

panel a d g and they looks uh very

panel a d g and they looks uh very
consistent and this is for the set node

consistent and this is for the set node

consistent and this is for the set node
system and here also did the same thing

system and here also did the same thing

system and here also did the same thing
for other uh the other two typical uh uh

for other uh the other two typical uh uh

for other uh the other two typical uh uh
systems uh for the compost boom system

systems uh for the compost boom system

systems uh for the compost boom system
uh we use different forcing rates and uh

uh we use different forcing rates and uh

uh we use different forcing rates and uh
we can get the same the same conclusion

we can get the same the same conclusion

we can get the same the same conclusion
as the S node system but for the boting

as the S node system but for the boting

as the S node system but for the boting
system

system

system
yeah honestly here um it's it's it's

yeah honestly here um it's it's it's

yeah honestly here um it's it's it's
really different for panel B and panel E

really different for panel B and panel E

really different for panel B and panel E
when we use different uh forcing rate to

when we use different uh forcing rate to

when we use different uh forcing rate to
train the model and uh yeah for this uh

train the model and uh yeah for this uh

train the model and uh yeah for this uh
point for this phenomena uh we we

point for this phenomena uh we we

point for this phenomena uh we we
thought is because the boting system

thought is because the boting system

thought is because the boting system
basically it's very it's uh a lot

basically it's very it's uh a lot

basically it's very it's uh a lot
of it's uh it's it has has a lot of uh

of it's uh it's it has has a lot of uh

of it's uh it's it has has a lot of uh
complicated uh chaotic ulations in in

complicated uh chaotic ulations in in

complicated uh chaotic ulations in in
itself so in this case um like in panel

itself so in this case um like in panel

itself so in this case um like in panel
B when we train the train train the

B when we train the train train the

B when we train the train train the
depending model on fix forcing rate for

depending model on fix forcing rate for

depending model on fix forcing rate for
other forcing rat the chaotic

other forcing rat the chaotic

other forcing rat the chaotic
occilations behavior is really different

occilations behavior is really different

occilations behavior is really different
we thought this is uh this uh chaotic

we thought this is uh this uh chaotic

we thought this is uh this uh chaotic
occilations will disturb the uh uh will

occilations will disturb the uh uh will

occilations will disturb the uh uh will
disturb the prediction of the deing

disturb the prediction of the deing

disturb the prediction of the deing
model and but in if we fit all the time

model and but in if we fit all the time

model and but in if we fit all the time
Ser forcing race time series into the

Ser forcing race time series into the

Ser forcing race time series into the
mod train the model and make prediction

mod train the model and make prediction

mod train the model and make prediction
on the testing data set then uh it can

on the testing data set then uh it can

on the testing data set then uh it can
give us a a looks uh much um much more

give us a a looks uh much um much more

give us a a looks uh much um much more
comfortable uh pattern uh in its

comfortable uh pattern uh in its

comfortable uh pattern uh in its
accuracy

accuracy

accuracy
and yeah here is this means uh when we

and yeah here is this means uh when we

and yeah here is this means uh when we
Trend this is also important for uh for

Trend this is also important for uh for

Trend this is also important for uh for
us uh in in the future if we want to

us uh in in the future if we want to

us uh in in the future if we want to
train a deing model we should consider

train a deing model we should consider

train a deing model we should consider
uh for a specific uh dynamical system

uh for a specific uh dynamical system

uh for a specific uh dynamical system
its internal Dynamics could Al could

its internal Dynamics could Al could

its internal Dynamics could Al could
potentially disturb the deing uh

potentially disturb the deing uh

potentially disturb the deing uh
indicator this need to be uh careful

indicator this need to be uh careful

indicator this need to be uh careful
yeah uh and then second uh second

yeah uh and then second uh second

yeah uh and then second uh second
analyze is for the uh prediction of the

analyze is for the uh prediction of the

analyze is for the uh prediction of the
out of sample dynamical systems uh that

out of sample dynamical systems uh that

out of sample dynamical systems uh that
means um for the three dynamical system

means um for the three dynamical system

means um for the three dynamical system
set node Bing and composed boom uh

set node Bing and composed boom uh

set node Bing and composed boom uh
the here we plot the autocorrelation

the here we plot the autocorrelation

the here we plot the autocorrelation
function of the time serious uh

function of the time serious uh

function of the time serious uh
respectively from this this three system

respectively from this this three system

respectively from this this three system
systems and we can observe of the um

systems and we can observe of the um

systems and we can observe of the um
the uh there is some uh time scale

the uh there is some uh time scale

the uh there is some uh time scale
separation between this uh s uh systems

separation between this uh s uh systems

separation between this uh s uh systems
this means the dynamical dynamical

this means the dynamical dynamical

this means the dynamical dynamical
Dynamics of the three systems are

Dynamics of the three systems are

Dynamics of the three systems are
largely different from one another uh

largely different from one another uh

largely different from one another uh
but here we still perform a uh

but here we still perform a uh

but here we still perform a uh
interesting experiment for example for

interesting experiment for example for

interesting experiment for example for
the sod system we train the S train the

the sod system we train the S train the

the sod system we train the S train the
depending model on I fixed uh foring

depending model on I fixed uh foring

depending model on I fixed uh foring
rate uh a a certain foring rate uh from

rate uh a a certain foring rate uh from

rate uh a a certain foring rate uh from
the set not system then make prediction

the set not system then make prediction

the set not system then make prediction
for other foring rates and also for the

for other foring rates and also for the

for other foring rates and also for the
other foring rates in the uh uh in the

other foring rates in the uh uh in the

other foring rates in the uh uh in the
Bing system and the composed system

Bing system and the composed system

Bing system and the composed system
Let's uh let's look at a panel a b c uh

Let's uh let's look at a panel a b c uh

Let's uh let's look at a panel a b c uh
this means

this means

this means
uh and and we can still observe some uh

uh and and we can still observe some uh

uh and and we can still observe some uh
some uh some skill for prediction but

some uh some skill for prediction but

some uh some skill for prediction but
also it's very close to the Tipping

also it's very close to the Tipping

also it's very close to the Tipping
happen uh uh tipping times but but still

happen uh uh tipping times but but still

happen uh uh tipping times but but still
this means uh hopefully this uh this uh

this means uh hopefully this uh this uh

this means uh hopefully this uh this uh
deing could make some out of sample

deing could make some out of sample

deing could make some out of sample
prediction on make some prediction scale

prediction on make some prediction scale

prediction on make some prediction scale
for prediction under out of sample

for prediction under out of sample

for prediction under out of sample
dynamical systems and uh here we we also

dynamical systems and uh here we we also

dynamical systems and uh here we we also
did the same thing for the for the other

did the same thing for the for the other

did the same thing for the for the other
uh two dynamical systems and it seems

uh two dynamical systems and it seems

uh two dynamical systems and it seems
it's very interesting like the uh B for

it's very interesting like the uh B for

it's very interesting like the uh B for
the boting system the depending model

the boting system the depending model

the boting system the depending model
trended based on boting system it can

trended based on boting system it can

trended based on boting system it can
work very well for the composed boom

work very well for the composed boom

work very well for the composed boom
system and uh this pattern if we have

system and uh this pattern if we have

system and uh this pattern if we have
looked at the pattern F and I the Bing

looked at the pattern F and I the Bing

looked at the pattern F and I the Bing
the boting systems de planing model can

the boting systems de planing model can

the boting systems de planing model can
make very well prediction for the

make very well prediction for the

make very well prediction for the
compost boom system and the pattern are

compost boom system and the pattern are

compost boom system and the pattern are
very similar to each other uh this means

very similar to each other uh this means

very similar to each other uh this means
although the dynamic Dynamics are

although the dynamic Dynamics are

although the dynamic Dynamics are
different but it can still make skill

different but it can still make skill

different but it can still make skill
for prediction sometimes and uh uh yeah

for prediction sometimes and uh uh yeah

for prediction sometimes and uh uh yeah
uh finally we also uh did a uh uh we

uh finally we also uh did a uh uh we

uh finally we also uh did a uh uh we
also trans the TR our deping model trans

also trans the TR our deping model trans

also trans the TR our deping model trans
deping model in include all the forcing

deping model in include all the forcing

deping model in include all the forcing
rates and all the uh time the time Ser

rates and all the uh time the time Ser

rates and all the uh time the time Ser
from all the system all the three

from all the system all the three

from all the system all the three
systems and then the this is we call it

systems and then the this is we call it

systems and then the this is we call it
a comprehensive deing model then

a comprehensive deing model then

a comprehensive deing model then
eventually this comprehensive deing

eventually this comprehensive deing

eventually this comprehensive deing
model can predict the uh yeah can

model can predict the uh yeah can

model can predict the uh yeah can
predict the uh uh wrting those tipping

predict the uh uh wrting those tipping

predict the uh uh wrting those tipping
very very well for different the three

very very well for different the three

very very well for different the three
different systems

yeah um um yeah uh it's very close to uh

yeah um um yeah uh it's very close to uh
to the final slides but yeah um here I I

to the final slides but yeah um here I I

to the final slides but yeah um here I I
want to also want to introduce some

want to also want to introduce some

want to also want to introduce some
interesting thing uh it's a perspective

interesting thing uh it's a perspective

interesting thing uh it's a perspective
from the explainable AI but uh yeah

from the explainable AI but uh yeah

from the explainable AI but uh yeah
um basically the explainable AI we could

um basically the explainable AI we could

um basically the explainable AI we could
regard we could associate it with is R

regard we could associate it with is R

regard we could associate it with is R
regression for example consider if we

regression for example consider if we

regression for example consider if we
have a r regression uh we use a r

have a r regression uh we use a r

have a r regression uh we use a r
regression model to fit uh based on a

regression model to fit uh based on a

regression model to fit uh based on a
lot of exp explainable variables then

lot of exp explainable variables then

lot of exp explainable variables then
for each variables explainable variables

for each variables explainable variables

for each variables explainable variables
we could have the feature importance

we could have the feature importance

we could have the feature importance
based on the fitting uh efficience of

based on the fitting uh efficience of

based on the fitting uh efficience of
the r regression model uh here for the s

the r regression model uh here for the s

the r regression model uh here for the s
model uh it's the same we can here we

model uh it's the same we can here we

model uh it's the same we can here we
just take the uh layer uh layer

just take the uh layer uh layer

just take the uh layer uh layer
relevance propagation algorithm to

relevance propagation algorithm to

relevance propagation algorithm to
extract the uh feature importance uh of

extract the uh feature importance uh of

extract the uh feature importance uh of
each uh input data uh this could yeah

each uh input data uh this could yeah

each uh input data uh this could yeah
just regard it just associate it uh with

just regard it just associate it uh with

just regard it just associate it uh with
the r regression featureing importance

the r regression featureing importance

the r regression featureing importance
uh this would be very similar diagram

uh this would be very similar diagram

uh this would be very similar diagram
but here uh it's a prediction for the

but here uh it's a prediction for the

but here uh it's a prediction for the
set node system and just 30 time steps

set node system and just 30 time steps

set node system and just 30 time steps
before the RTP happens then if we

before the RTP happens then if we

before the RTP happens then if we
compare the uh uh layerwise propagation

compare the uh uh layerwise propagation

compare the uh uh layerwise propagation
lrp score uh before uh for different

lrp score uh before uh for different

lrp score uh before uh for different
time series uh for different uh

time series uh for different uh

time series uh for different uh
different point of the time Ser along

different point of the time Ser along

different point of the time Ser along
the time series then uh we expect to

the time series then uh we expect to

the time series then uh we expect to
find out some precursor signal uh heed

find out some precursor signal uh heed

find out some precursor signal uh heed
in in the time seral segments at

in in the time seral segments at

in in the time seral segments at
different time lead time uh forecast

different time lead time uh forecast

different time lead time uh forecast
lead time for example here if we compare

lead time for example here if we compare

lead time for example here if we compare
the uh compare aring and nontipping

the uh compare aring and nontipping

the uh compare aring and nontipping
categories of the for the lrp score we

categories of the for the lrp score we

categories of the for the lrp score we
can find it's very different and

can find it's very different and

can find it's very different and
specifically we find two uh difference

specifically we find two uh difference

specifically we find two uh difference
uh fature feature importance one is very

uh fature feature importance one is very

uh fature feature importance one is very
close to the Tipping uh the end of the

close to the Tipping uh the end of the

close to the Tipping uh the end of the
time series segment this is uh

time series segment this is uh

time series segment this is uh
comparably easy to understand because

comparably easy to understand because

comparably easy to understand because
this means the tping uh the r tping r

this means the tping uh the r tping r

this means the tping uh the r tping r
tping probability are highly related to

tping probability are highly related to

tping probability are highly related to
the uh the current time step the current

the uh the current time step the current

the uh the current time step the current
time point of the system State for the

time point of the system State for the

time point of the system State for the
system state but Al also we find a

system state but Al also we find a

system state but Al also we find a
fingerprint uh it's a fixed fingerprint

fingerprint uh it's a fixed fingerprint

fingerprint uh it's a fixed fingerprint
uh

uh

uh
uh around around a uh time window uh

uh around around a uh time window uh

uh around around a uh time window uh
that is uh um 50 times dep to 100 times

that is uh um 50 times dep to 100 times

that is uh um 50 times dep to 100 times
dep uh before the arping happens and we

dep uh before the arping happens and we

dep uh before the arping happens and we
notice this peak and for this peak it's

notice this peak and for this peak it's

notice this peak and for this peak it's
very interesting where uh we realize

very interesting where uh we realize

very interesting where uh we realize
it's uh it there must be some dynamical

it's uh it there must be some dynamical

it's uh it there must be some dynamical
features can be uh already captured by

features can be uh already captured by

features can be uh already captured by
the deing model then there is a peak

the deing model then there is a peak

the deing model then there is a peak
here so basically for the uh uh for the

here so basically for the uh uh for the

here so basically for the uh uh for the
model for the deping uh for the RTP uh

model for the deping uh for the RTP uh

model for the deping uh for the RTP uh
uh for the RTP here uh there are two

uh for the RTP here uh there are two

uh for the RTP here uh there are two
elements uh for the RTP one is the

elements uh for the RTP one is the

elements uh for the RTP one is the
forcing rate second second uh second one

forcing rate second second uh second one

forcing rate second second uh second one
is the uh is the noise pations but for

is the uh is the noise pations but for

is the uh is the noise pations but for
the noise pations we checked it but not

the noise pations we checked it but not

the noise pations we checked it but not
but we didn't find any special thing

but we didn't find any special thing

but we didn't find any special thing
related to this fingerprint but for the

related to this fingerprint but for the

related to this fingerprint but for the
foring rate we found some interesting

foring rate we found some interesting

foring rate we found some interesting
thing here uh because the time serious

thing here uh because the time serious

thing here uh because the time serious
uh the time series here they have

uh the time series here they have

uh the time series here they have
different uh maximal uh foring rates

different uh maximal uh foring rates

different uh maximal uh foring rates
maximal that is the uh uh just now here

maximal that is the uh uh just now here

maximal that is the uh uh just now here
for the forcing profile if we calculate

for the forcing profile if we calculate

for the forcing profile if we calculate
the

the

the
difference uh difference time series of

difference uh difference time series of

difference uh difference time series of
the the foring profile then we can get

the the foring profile then we can get

the the foring profile then we can get
the instant forcing rate also yeah it's

the instant forcing rate also yeah it's

the instant forcing rate also yeah it's
instant shift rate also then we

instant shift rate also then we

instant shift rate also then we
can we just make a composition and find

can we just make a composition and find

can we just make a composition and find
uh some early R tping and The Late Late

uh some early R tping and The Late Late

uh some early R tping and The Late Late
RTP that means the early or late is

RTP that means the early or late is

RTP that means the early or late is
comparably defined by the Yeah the

comparably defined by the Yeah the

comparably defined by the Yeah the
maximum of the instant forcing

maximum of the instant forcing

maximum of the instant forcing
rate for example like the early RTP The

rate for example like the early RTP The

rate for example like the early RTP The
Tipping tipping time is very close to

Tipping tipping time is very close to

Tipping tipping time is very close to
the maximal uh maximal forcing rate uh

the maximal uh maximal forcing rate uh

the maximal uh maximal forcing rate uh
usually for the uh in previous studies

usually for the uh in previous studies

usually for the uh in previous studies
people would think would s would think

people would think would s would think

people would think would s would think
when the uh for external forcing reach

when the uh for external forcing reach

when the uh for external forcing reach
is maximum forcing rate this is most

is maximum forcing rate this is most

is maximum forcing rate this is most
dangerous for the uh most dangerous

dangerous for the uh most dangerous

dangerous for the uh most dangerous
period for the system to undergo to have

period for the system to undergo to have

period for the system to undergo to have
a tipping points uh but here we with

a tipping points uh but here we with

a tipping points uh but here we with
find that it's relatively late to the

find that it's relatively late to the

find that it's relatively late to the
maximum forcing uh but uh we also find

maximum forcing uh but uh we also find

maximum forcing uh but uh we also find
another uh some other uh samples uh the

another uh some other uh samples uh the

another uh some other uh samples uh the
Tipping time is much much more late much

Tipping time is much much more late much

Tipping time is much much more late much
later than the maximal forcing uh rate

later than the maximal forcing uh rate

later than the maximal forcing uh rate
and uh here if we the forcing rate uh if

and uh here if we the forcing rate uh if

and uh here if we the forcing rate uh if
we have looked at forcing rate it's

we have looked at forcing rate it's

we have looked at forcing rate it's
exactly uh sh the C

exactly uh sh the C

exactly uh sh the C
time window with the fingerprint

time window with the fingerprint

time window with the fingerprint
here yeah and uh uh finally we also uh

here yeah and uh uh finally we also uh

here yeah and uh uh finally we also uh
have a look we also want to talk about

have a look we also want to talk about

have a look we also want to talk about
something about the selection of the uh

something about the selection of the uh

something about the selection of the uh
Naro Network architecture because I

Naro Network architecture because I

Naro Network architecture because I
mentioned uh we just use a very simple

mentioned uh we just use a very simple

mentioned uh we just use a very simple
thing and and somebody would argue oh

thing and and somebody would argue oh

thing and and somebody would argue oh
why why just use a very simple thing and

why why just use a very simple thing and

why why just use a very simple thing and
it's uh it's a old dog but but I have to

it's uh it's a old dog but but I have to

it's uh it's a old dog but but I have to
say the Naro Network s is very powerful

say the Naro Network s is very powerful

say the Naro Network s is very powerful
but it's simple uh if we select a simple

but it's simple uh if we select a simple

but it's simple uh if we select a simple
naral Network architecture then this

naral Network architecture then this

naral Network architecture then this
could be uh helpful for the community to

could be uh helpful for the community to

could be uh helpful for the community to
understand it but here we also uh uh we

understand it but here we also uh uh we

understand it but here we also uh uh we
also compel it way compare different

also compel it way compare different

also compel it way compare different
just take took different Naro Network

just take took different Naro Network

just take took different Naro Network
architectures like the LM and also the

architectures like the LM and also the

architectures like the LM and also the
uh MLP or self attention mechanism and

uh MLP or self attention mechanism and

uh MLP or self attention mechanism and
then makes the prediction this is the

then makes the prediction this is the

then makes the prediction this is the
our curve of the prediction results uh

our curve of the prediction results uh

our curve of the prediction results uh
it seems uh s in lstm or the combination

it seems uh s in lstm or the combination

it seems uh s in lstm or the combination
of LM CN uh this is exactly Thomas Barry

of LM CN uh this is exactly Thomas Barry

of LM CN uh this is exactly Thomas Barry
ever used in his P paper and also

ever used in his P paper and also

ever used in his P paper and also
compare with and also the self attention

compare with and also the self attention

compare with and also the self attention
they have the comp terrible prediction

they have the comp terrible prediction

they have the comp terrible prediction
ability uh maybe for the boting system

ability uh maybe for the boting system

ability uh maybe for the boting system
uh it's chaotic uh Dynamics uh really

uh it's chaotic uh Dynamics uh really

uh it's chaotic uh Dynamics uh really
dist uh uh disturb the performance of

dist uh uh disturb the performance of

dist uh uh disturb the performance of
the MLP but here yeah we uh anyway we

the MLP but here yeah we uh anyway we

the MLP but here yeah we uh anyway we
could we could conclude that uh PR de

could we could conclude that uh PR de

could we could conclude that uh PR de
planing indicator actually it's

planing indicator actually it's

planing indicator actually it's
independent on as specific naron net nwk

independent on as specific naron net nwk

independent on as specific naron net nwk
architecture we can in the future we can

architecture we can in the future we can

architecture we can in the future we can
even consider a more uh comprehensive or

even consider a more uh comprehensive or

even consider a more uh comprehensive or
complicated architecture like

complicated architecture like

complicated architecture like
Transformer or or generative uh deing

Transformer or or generative uh deing

Transformer or or generative uh deing
model to yeah to get maybe can get

model to yeah to get maybe can get

model to yeah to get maybe can get
better results but here the same thing

better results but here the same thing

better results but here the same thing
is also works very well and it's

is also works very well and it's

is also works very well and it's
efficient in

efficient in

efficient in
computation uh yeah yeah and and I

computation uh yeah yeah and and I

computation uh yeah yeah and and I
I I also want to uh highlight some some

I I also want to uh highlight some some

I I also want to uh highlight some some
useful thing for the depending uh uh

useful thing for the depending uh uh

useful thing for the depending uh uh
indicator for the we know for the

indicator for the we know for the

indicator for the we know for the
critical slowing down it's always

critical slowing down it's always

critical slowing down it's always
calculated based on the uh time serious

calculated based on the uh time serious

calculated based on the uh time serious
articulation and variance and this means

articulation and variance and this means

articulation and variance and this means
we usually even though we for a specific

we usually even though we for a specific

we usually even though we for a specific
system like Arctic uh like the an an

system like Arctic uh like the an an

system like Arctic uh like the an an
Atlantic illation uh illation o ocean

Atlantic illation uh illation o ocean

Atlantic illation uh illation o ocean
illation we we could have a lot of

illation we we could have a lot of

illation we we could have a lot of
multiple um we could have a multiple

multiple um we could have a multiple

multiple um we could have a multiple
time Ser for for it but usually we can

time Ser for for it but usually we can

time Ser for for it but usually we can
only calculate credit cost Lo Down based

only calculate credit cost Lo Down based

only calculate credit cost Lo Down based
one of the time series and but here for

one of the time series and but here for

one of the time series and but here for
the deing model we can just simply add

the deing model we can just simply add

the deing model we can just simply add
the uh add more uh explainable uh more

the uh add more uh explainable uh more

the uh add more uh explainable uh more
dynamical variables into the CM just at

dynamical variables into the CM just at

dynamical variables into the CM just at
simply at one additional Channel then we

simply at one additional Channel then we

simply at one additional Channel then we
could make the prediction uh

could make the prediction uh

could make the prediction uh
for by by involving more uh dynamical

for by by involving more uh dynamical

for by by involving more uh dynamical
variables but here it seems uh for the

variables but here it seems uh for the

variables but here it seems uh for the
boting system compos boom system they

boting system compos boom system they

boting system compos boom system they
also have a multiple multiple dynamical

also have a multiple multiple dynamical

also have a multiple multiple dynamical
variables but if we include them them

variables but if we include them them

variables but if we include them them
into the uh de planning prediction it

into the uh de planning prediction it

into the uh de planning prediction it
seems It's comparable to the uh yeah a

seems It's comparable to the uh yeah a

seems It's comparable to the uh yeah a
single variable based uh

single variable based uh

single variable based uh
indicator yeah this is the last slide

indicator yeah this is the last slide

indicator yeah this is the last slide
and uh yeah it's a short summary but uh

and uh yeah it's a short summary but uh

and uh yeah it's a short summary but uh
I really want to talk something uh here

I really want to talk something uh here

I really want to talk something uh here
this could be yeah this could be useful

this could be yeah this could be useful

this could be yeah this could be useful
uh for our future work firstly we know

uh for our future work firstly we know

uh for our future work firstly we know
the uh de planning uh the planning can

the uh de planning uh the planning can

the uh de planning uh the planning can
advance our ability to predict raing de

advance our ability to predict raing de

advance our ability to predict raing de
tping and noise induc tping and uh then

tping and noise induc tping and uh then

tping and noise induc tping and uh then
we can just uh get make use of the

we can just uh get make use of the

we can just uh get make use of the
experience of emble realizations and

experience of emble realizations and

experience of emble realizations and
just make you uh just apply the them

just make you uh just apply the them

just make you uh just apply the them
into the influence on individual time

into the influence on individual time

into the influence on individual time
series and also we find uh the deing

series and also we find uh the deing

series and also we find uh the deing
model can have good transferability

model can have good transferability

model can have good transferability
across uh across different out of sample

across uh across different out of sample

across uh across different out of sample
forcing rates and out of sample

forcing rates and out of sample

forcing rates and out of sample
dynamical system

dynamical system

dynamical system
but of course if we train all the models

but of course if we train all the models

but of course if we train all the models
together

together

together
overall we must can we can must get a

overall we must can we can must get a

overall we must can we can must get a
very uh comprehensive deing model and

very uh comprehensive deing model and

very uh comprehensive deing model and
very powerful but in the future um it's

very powerful but in the future um it's

very powerful but in the future um it's
promising uh for us uh to predict

promising uh for us uh to predict

promising uh for us uh to predict
tipping uh across the critical forcing

tipping uh across the critical forcing

tipping uh across the critical forcing
value this is bation tipping diagram and

value this is bation tipping diagram and

value this is bation tipping diagram and
also in addition the uh critical forcing

also in addition the uh critical forcing

also in addition the uh critical forcing
rates and uh then we can yeah we

rates and uh then we can yeah we

rates and uh then we can yeah we
hopefully

hopefully

hopefully
um we hopefully compare to the critical

um we hopefully compare to the critical

um we hopefully compare to the critical
slowing down we can have much more

slowing down we can have much more

slowing down we can have much more
comprehensive early warning indicator

comprehensive early warning indicator

comprehensive early warning indicator
also make of the explan explainable AI

also make of the explan explainable AI

also make of the explan explainable AI
algorithm we could discover more

algorithm we could discover more

algorithm we could discover more
Fingerprints of the Tipping points for

Fingerprints of the Tipping points for

Fingerprints of the Tipping points for
some specific um systems like the um

some specific um systems like the um

some specific um systems like the um
Antarctic ocean o

Antarctic ocean o

Antarctic ocean o
occilations this is very Wishful and we

occilations this is very Wishful and we

occilations this is very Wishful and we
really want to um uh further focus on

really want to um uh further focus on

really want to um uh further focus on
this points but of course uh there is

this points but of course uh there is

this points but of course uh there is
still open question here because just

still open question here because just

still open question here because just
now uh

now uh

now uh
the the the Tipping uh early warning uh

the the the Tipping uh early warning uh

the the the Tipping uh early warning uh
indicator is based on the Tipping probab

indicator is based on the Tipping probab

indicator is based on the Tipping probab
probability it's basically it's it's

probability it's basically it's it's

probability it's basically it's it's
aesthetic a matric uh but uh of course

aesthetic a matric uh but uh of course

aesthetic a matric uh but uh of course
alter alternatively uh we could also

alter alternatively uh we could also

alter alternatively uh we could also
have a tipping trajectory prediction

have a tipping trajectory prediction

have a tipping trajectory prediction
that is uh stand on current climate we

that is uh stand on current climate we

that is uh stand on current climate we
want we can we maybe we want also want

want we can we maybe we want also want

want we can we maybe we want also want
to predict the time seral the uh EV time

to predict the time seral the uh EV time

to predict the time seral the uh EV time
uh evolutional uh trajectory in the

uh evolutional uh trajectory in the

uh evolutional uh trajectory in the
future scenario and this is the teing

future scenario and this is the teing

future scenario and this is the teing
trajectory but currently in in our de

trajectory but currently in in our de

trajectory but currently in in our de
planning model architecture this cannot

planning model architecture this cannot

planning model architecture this cannot
is is not un achievable but in a very

is is not un achievable but in a very

is is not un achievable but in a very
recent paper published in uh physical

recent paper published in uh physical

recent paper published in uh physical
review uh uh research and also uh last

review uh uh research and also uh last

review uh uh research and also uh last
just last out of out in last month and

just last out of out in last month and

just last out of out in last month and
uh they they already tried to do

uh they they already tried to do

uh they they already tried to do
something along this direction but we

something along this direction but we

something along this direction but we
really hope this this all the progress

really hope this this all the progress

really hope this this all the progress
could help us to better to help us in uh

could help us to better to help us in uh

could help us to better to help us in uh
serve for the um tpping points uh

serve for the um tpping points uh

serve for the um tpping points uh
Community yeah and this is my email if

Community yeah and this is my email if

Community yeah and this is my email if
you are interested and uh just feel free

you are interested and uh just feel free

you are interested and uh just feel free
to contact me and also uh last week our

to contact me and also uh last week our

to contact me and also uh last week our
paper was uh p uh was published out uh

paper was uh p uh was published out uh

paper was uh p uh was published out uh
in nature machine intelligence and uh if

in nature machine intelligence and uh if

in nature machine intelligence and uh if
you want to know more details yeah you

you want to know more details yeah you

you want to know more details yeah you
could also yeah find more in in that

could also yeah find more in in that

could also yeah find more in in that
paper yeah thank you much I think I'm

paper yeah thank you much I think I'm

paper yeah thank you much I think I'm
done thank you for your time yeah thank

done thank you for your time yeah thank

done thank you for your time yeah thank
you very much thank you any questions or

comments yes I

comments yes I
yeah I'm assuming you mean me yeah yeah

yeah I'm assuming you mean me yeah yeah

yeah I'm assuming you mean me yeah yeah
sorry sorry I me Lou yeah sorry okay

sorry sorry I me Lou yeah sorry okay

sorry sorry I me Lou yeah sorry okay
yeah yeah interesting talk uh I'm aware

yeah yeah interesting talk uh I'm aware

yeah yeah interesting talk uh I'm aware
of a recent paper by yining live the

of a recent paper by yining live the

of a recent paper by yining live the
Arizona State University and his group

Arizona State University and his group

Arizona State University and his group
looking at uh the critical point at

looking at uh the critical point at

looking at uh the critical point at
which uh a crisis happens in a chaotic

which uh a crisis happens in a chaotic

which uh a crisis happens in a chaotic
attractor as you vary a parameter in the

attractor as you vary a parameter in the

attractor as you vary a parameter in the
system yes and they did this they did

system yes and they did this they did

system yes and they did this they did
this um learning of that using a

this um learning of that using a

this um learning of that using a
reservoir computer and they did a pretty

reservoir computer and they did a pretty

reservoir computer and they did a pretty
good job of telling where that was going

good job of telling where that was going

good job of telling where that was going
to happen uh unlike your there was no

to happen uh unlike your there was no

to happen uh unlike your there was no
noise on it uh I recall anyway uh

noise on it uh I recall anyway uh

noise on it uh I recall anyway uh
however they did Miss uh they could not

however they did Miss uh they could not

however they did Miss uh they could not
predict a window in the chaotic system

predict a window in the chaotic system

predict a window in the chaotic system
I'm wondering uh if you have tried a

I'm wondering uh if you have tried a

I'm wondering uh if you have tried a
chaotic system something like that and

chaotic system something like that and

chaotic system something like that and
tried to predict a u a bifurcation and

tried to predict a u a bifurcation and

tried to predict a u a bifurcation and
whether you've looked into using

whether you've looked into using

whether you've looked into using
Reservoir computers rather than a neural

Reservoir computers rather than a neural

Reservoir computers rather than a neural
network yeah yeah thank you uh I think

network yeah yeah thank you uh I think

network yeah yeah thank you uh I think
this uh the paper you mentioned exactly

this uh the paper you mentioned exactly

this uh the paper you mentioned exactly
I exactly the paper here okay yeah I

I exactly the paper here okay yeah I

I exactly the paper here okay yeah I
point here yeah we also already noticed

point here yeah we also already noticed

point here yeah we also already noticed
it is very it's very amazing um yeah

it is very it's very amazing um yeah

it is very it's very amazing um yeah
firstly for your uh for your question

firstly for your uh for your question

firstly for your uh for your question
let's focus on your questions uh firstly

let's focus on your questions uh firstly

let's focus on your questions uh firstly
um way uh we for our de planning model

um way uh we for our de planning model

um way uh we for our de planning model
CM based indicator we have not tried for

CM based indicator we have not tried for

CM based indicator we have not tried for
the bation tipping but yeah the reason

the bation tipping but yeah the reason

the bation tipping but yeah the reason
is this is already done by Thomas bur uh

is this is already done by Thomas bur uh

is this is already done by Thomas bur uh
he he has a p publication on pns it's um

he he has a p publication on pns it's um

he he has a p publication on pns it's um
2021 and uh he already demonstrates

2021 and uh he already demonstrates

2021 and uh he already demonstrates
using a lstm plus c architecture here uh

using a lstm plus c architecture here uh

using a lstm plus c architecture here uh
can achieve very nice prediction results

can achieve very nice prediction results

can achieve very nice prediction results
for the bation Tipping even for the uh

for the bation Tipping even for the uh

for the bation Tipping even for the uh
yeah I mean I I know maybe you mean a

yeah I mean I I know maybe you mean a

yeah I mean I I know maybe you mean a
specific chaotic system like the bation

specific chaotic system like the bation

specific chaotic system like the bation
in the

in the

in the
Lawrence 63 system maybe it's yeah I

Lawrence 63 system maybe it's yeah I

Lawrence 63 system maybe it's yeah I
noticed in uh in ch Li group they also

noticed in uh in ch Li group they also

noticed in uh in ch Li group they also
uh have the yeah have a paper about this

uh have the yeah have a paper about this

uh have the yeah have a paper about this
point about this direction but yeah

point about this direction but yeah

point about this direction but yeah
thank you uh we will consider about this

thank you uh we will consider about this

thank you uh we will consider about this
a specific CL uh chaotic system but uh

a specific CL uh chaotic system but uh

a specific CL uh chaotic system but uh
also we have not tried it but uh I I

also we have not tried it but uh I I

also we have not tried it but uh I I
trust I I I would believe uh San could

trust I I I would believe uh San could

trust I I I would believe uh San could
work for it because uh because here uh

work for it because uh because here uh

work for it because uh because here uh
we have the boting system the boting

we have the boting system the boting

we have the boting system the boting
system itself is already very C have a

system itself is already very C have a

system itself is already very C have a
very uh a lot of have a various uh

very uh a lot of have a various uh

very uh a lot of have a various uh
chaotic oscillations in this boting

chaotic oscillations in this boting

chaotic oscillations in this boting
system

system

system
so here our model works for boting

so here our model works for boting

so here our model works for boting
system then I yeah I would believe it

system then I yeah I would believe it

system then I yeah I would believe it
can also work for the LA

can also work for the LA

can also work for the LA
system thank you very much but yeah

system thank you very much but yeah

system thank you very much but yeah
thank you yeah but also maybe for

thank you yeah but also maybe for

thank you yeah but also maybe for
another question uh maybe your related

another question uh maybe your related

another question uh maybe your related
to your question uh is the like the uh

to your question uh is the like the uh

to your question uh is the like the uh
in uh inance group uh they uh your

in uh inance group uh they uh your

in uh inance group uh they uh your
Reservoir computer is also very

Reservoir computer is also very

Reservoir computer is also very
efficient in computation and uh uh it

efficient in computation and uh uh it

efficient in computation and uh uh it
can predict the trajectory tipping

can predict the trajectory tipping

can predict the trajectory tipping
trajectory and uh uh but but based on

trajectory and uh uh but but based on

trajectory and uh uh but but based on
the uh recent two paper

the uh recent two paper

the uh recent two paper
Publications uh we have a very close uh

Publications uh we have a very close uh

Publications uh we have a very close uh
look at the paper uh they yeah and they

look at the paper uh they yeah and they

look at the paper uh they yeah and they
they already did a lot of nice work on

they already did a lot of nice work on

they already did a lot of nice work on
the bation tipping but since they have

the bation tipping but since they have

the bation tipping but since they have
not done uh test if it also works for

not done uh test if it also works for

not done uh test if it also works for
the WR tipping but yeah I'm also very

the WR tipping but yeah I'm also very

the WR tipping but yeah I'm also very
curious if it were yeah what will

curious if it were yeah what will

curious if it were yeah what will
happens when using Reservoir computer

happens when using Reservoir computer

happens when using Reservoir computer
predicts the Tipping trajectory uh in

predicts the Tipping trajectory uh in

predicts the Tipping trajectory uh in
rping diagram this could be very amazing

rping diagram this could be very amazing

rping diagram this could be very amazing
yeah yeah thank you

questions all right seems not yeah thank

questions all right seems not yeah thank
you very much you for coming and thanks

you very much you for coming and thanks

you very much you for coming and thanks
again for the nice talk and thanks all

again for the nice talk and thanks all

again for the nice talk and thanks all
for for coming yeah see you next week

for for coming yeah see you next week

for for coming yeah see you next week
yeah byebye yeah byebye