Sequential Data Assimilation:

(1)

Sequential Data Assimilation:

Online Information Fusion Platform for Simulation and Observation Data

Simulation and Observation Data

R h O i ti f I f ti d S t

Research Organization of Information and Systems The Institute of Statistical Mathematics/JST CREST* f

Tomoyuki Higuchi

*

^Japan^ScienceTechnology Agency CoreResearch forEvolutionalScience andTechnology

1

CoreResearch forEvolutionalScience andTechnology

TESD: Four Kind of Methodology of Science

Deductive Approach

Inductive Approach

Approach Approach

S:Simulation D䠖Massive

(Axle)

Data Assimilation

Cyber-space

Data Analysis

Მ Analysis

T:Theory E:Experiment

Drive Force for Science

(2)

Outline

1. Simulations with uncertainties 2 Data Assimilation (DA)

2. Data Assimilation (DA) 3. Modeling uncertainties

4 Sequential DA and generalized state space model 4. Sequential DA and generalized state space model 5. Ensemble-based nonlinear filtering methods

1 Ensemble Kalman filter 1. Ensemble Kalman filter 2. Particle filter

6. Applications with peta-scale computing pp p p g

1. Tsunami Simulation model 2. Ocean Tide Simulation 3. Genome Science

7. Next generation of supercomputer

8 C l i

3

8. Conclusions

Construction of Simulation Model

䠄simplified meteorological model around Japan䠅

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physical variable vector is assigned

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6

(4)

Simulation including uncertainty

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What is Data Assimilation ?

E i bj t i t l d h

Emerging subject in meteorology and oceanography.

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and observed data

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䠄e g 䠅Accurate weather forecast needs good initial conditions

䠄e.g.䠅Accurate weather forecast needs good initial conditions.

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Correct variables in numerical simulation model using observation data

using observation data.

= Data Assimilation

(5)

Objects of Data Assimilation from a viewpoint of Meteorology and Oceanography

[1] To produce the best (better) initial condition for forecasting. It is actually realized in the real weather forecast (ex., Japan Meteorological Agency).

Meteorology and Oceanography

[2] To find the best (better) boundary condition in constructing a simulation model. This procedure includes a setting of appropriate boundary conditions

f d li ith l d h

necessary for dealing with a coupled phenomena.

[3] To attain an optimal parameter vector that appears in an empirical law

( h ) l d f d ibi li t d h hi h

(scheme) employed for describing complicated phenomena which possesses the different time and spatial scales. A validation of the empirically given values is regarded as this problem.

[4] To inter/extrapolate (estimate) an physical quantity at times and locations without observations based on a numerical simulation model. This procedure LVFDOOHG³Dgeneration of re-analysis dataset (product)´7KLVGDWDVHWLVXVHG

g y

(p ) to discover a new scientific findings by general geophysical researchers.

[5] To conduct an experiment with a virtual observation network and perform a

[ ] p p

sensitivity analysis in an attempt to construct an effective observation

network system with less budgetary cost and less consuming time.

(ex. Kamachi et al., 2006)

Modeling uncertainties

R t id i t f t i t i h

Represent a wide variety of uncertainty in a research target by distribution function.

8QGHUVWDQGDFRPSOH[WDUJHWV127IURPLWVVLPSOH statistics such as mean, , %87IURPLWVGLVWULEXWLRQ directly.

N i f P b bili Th hi f b bili Notion of Probability: The machinery of probability

theory is used to describe the uncertainty in model parameters or choice of model itself

parameters or choice of model itself.

Probability theoryprovides a framework for quantification and manipulation of uncertainty We will introduce a basic concept of probability theory next uncertainty. We will introduce a basic concept of probability theory next.

(6)

Bayesian View

Central Role in Pattern Recognition and Machine Learning Data dist.䠄likelihood function䠅 Prior dist.

It expresses how probable the observed dataset is for different settings of the parameter vector X.

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We are interested in estimating a posterior

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distribution in most of circumstances.

We would like to be able to quantify our expression of uncertainty and make a precise revisions of uncertainty in the light of new evidence as well as subsequently to be able to take optimal actions/decisions as a consequence

evidence, as well as subsequently to be able to take optimal actions/decisions as a consequence.

Generative Model, Inversion with Bayes’ theorem, and Data Assimilation

and Data Assimilation

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Build a generative model and Use Bayes’ theorem

Latent Variables䠖xx

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Data Assimilation in Generalized State Space Model

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map nonlinear :

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Simulation system Large-scale observation

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(9)

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17

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Prediction Dist.

Sequential Data Assimilation

Estimate PDF of state vector or its moments (mean, variance, …) sequentially on each observation

x

t

) , , ,

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(10)

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(11)

Sequential DA Methodology

Ensemble Kalman Filter (EnKF) is widely used Ensemble Kalman Filter (EnKF) is widely used.

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21

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22

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(12)

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23

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Observation:

y t

likelihood

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(13)

Projects in progress

࣭Coupled Ocean-Atmosphere model

Genta Ueno (ISM/JST CREST) ( )

T. Kagimoto (JAMSTEC, FRCGC), N. Hirose (Kyushu Univ., RIAM)

࣭ Tsunami model

Kazuyuki Nakamura (JST CREST)

N. Hirose (Kyushu Univ., RIAM)

࣭Ocean tide

Daisuke Inazu (JST CREST)

T Sato S Miura (Tohoku Univ ) and others (Alaska Univ )

䞉3D structure of ring current

Shin ¶ ya Nakano (JST CREST),

T. Sato, S. Miura (Tohoku Univ.), and others (Alaska Univ.)

Shin ya Nakano (JST CREST),

Y. Ebihara (Nagoya Univ.) 䠈M.-C Fok (NASA) S.-I. Ohtani䠈P.C.Brandt䠄Johns Hopkins Univ.)

࣭Genome informatics

25

Genome informatics

Ryo Yoshida (ISM/JST CREST

) Miyano lab. (Tokyo Univ./IMS)

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Near Earth Space Ocean and 1AU

1 000k

Near Earth Space

䠄Ring Current䠅

Ocean and Atmosphere 1,000km

Ocean Tsunami Tide

1km

Data Assimilation in

O d A h i

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Ocean and Atmospheric SciencesĸLeading area

in DA researches䠅

1cm

Hour Day M th Y 100

(Measurement of gene and protein expressions)

26 26 26

Hour Day Month Year 100 years

(14)

Revisit : What is Data Assimilation?

Emerging subject in meteorology and oceanography

Emerging subject in meteorology and oceanography.

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6KDOORZ ZDWHU HTXDWLRQV PRGHO Tide gage data

27

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Tsunami Simulation Model

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6HDbottom

Uncertainty in measured water depth!

d

i

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28

(15)

Numerical Simulation (Not DA)

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Comparison of Sea Surface Displacement

SKKU DBDBV Displacement at 䠄cm䠅

10 20

10

0 0

-10 -10

-20

10 20 30 40

Time 䠄minute䠅

30

(16)

Observation Data

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Okushiri tsunami

(1993) ²⁰

40

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0 -20

Tide gage䠄cm䠅

0 50 100 150 200 250

20 -40

Time 䠄min䠅

Application to Real Data

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•The depths in and around Yamato Rises (area A) varies among 4 bottom topography data set

data set.

•Uncertainty is introduced into South Rises and around area as linear combination of 4 data sets combination of 4 data sets.

j: number of data sets

, 25

~

,

²

,

w d w N

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m

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Used tide gauge

(17)

DA result

Shallow

Deep

•South Rise might be shallower than public data.

33 33

•Deeper area exists in south slope.

Personalized Simulation 䠖

Aboundaryconditionisassimilatedtolocalinformation.

We introduce a local/personal information into a numerical simulation model and personalize the

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simulation for each location/person.

⁰

w

w w

t H

H t

K v

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Sea Bottom friction coefficient

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wt

2 di i l fl t

v䠖 2-dimensional flow vector Ș䠖 Water surface height

H䠖 Water depth䠈f䠖 Coriolis parameter

Ocean tide simulation by our CREST project

Alaska Southeastern region 34

(18)

Water level and Flow vectors

35

SealevelrangeisAbout㼼5m.Currentspeedis(much)morethan1m/satthemouth of

Chatham Strait.

Water level and flow vectors 䠄Closeup䠅

36

(19)

Result with GINA

ᵥᵣᵬᵟᴾᶇᶑᴾᶂᶃᶃᶎᶃᶐᴾᶇᶌᴾᵿᴾᶀᵿᶗᵌ

M ₂ component tide

Result with GINA

GENAshowsagreatperformancein representing an ocean tide.

representinganoceantide.

1 2 3 4 5

Amplitude

5 6

7

Phase

37

ISM

³⁷

Genomic Data Assimilation

Statistical framework to link simulation model and data

+

Simulation model Biological data

P-P interaction expression

Formulated by the generalized State Space Model System model t

t

f x v

x (

₁

, T )

System model

Observation model t

t t

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w Hx y

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: state vector at time

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t : system noise, : parameter vector, : simulation devise,

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38

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y

: observation vector at time

) , 0 (

~ ^N V

²

w

_t : observation noise

t , _H

: observation matrix,

(20)

Circadian Rhythm Model with HFPN

HFPN (Hybrid Functional Petri Net) : A graphical programming language suitable to model biological pathways and can be used for simulations

Circadian Rhythm Model

Circadian Model Represented by HFPN Circadian Rhythm Model

of Mouse

Fujii et al 2005

Parameters Fujii et al. 2005

) 0 ( , ), 0

( ₁₂

1 m

m

4 3 2 1,k ,k ,k k

:Initial values :Speeds

45 parameters (12 states), 4 observations

39 39 4

3 2 1,s ,s ,s s

2 2,V W

:Thresholds :Noise variances

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100,000,000 particles 䠄䠍൨䠅 100,000 particles:10୓

(21)

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100,000,000 particles 䠄䠍൨䠅 100,000 particles:10୓

Next-Generation of Supercomputer in Japan at Kobe

2008/11/26

Japanese Government will spend more than 1 billion US$ for this national project.

䕔Grand Challenge:

-- Nanotech

(Institute for Molecular Science)

-- Life Science

(RIKEN)

(22)

ḟୡ௦ィ⟬⛉Ꮫ◊✲㛤Ⓨ䝥䝻䜾䝷䝮䠄ᙜ㠃䠅 Development for next-generation simulation

software for whole human body

Next-Generation simulation R&D group for

software for whole human body

Next Generation simulation R&D group for integrating life form simulations

1 M l l l

Riken Next-Generation Supercomputer R&D center

1.Molecular scale

2.Cell scale

3.Body organ scale

6 B i d N

4. Data analysis fusion 5. Upgrading of basic software 6. Brain and Neuron

5. Upgrading of basic software

Data analysis fusion Team

Univ. Tokyo (Prof. Miyano) ISM (Higuchi)

Estimation of large-scale gene network and its

applications

Representative Development of data

assimilation technique for life science simulations

Estimation method for large-scale gene network

Bayesian information

fusion technique

Data assimilation

technique

Genetic linkage analysis

Haplotype analysis technique

Prediction technique for

Protein

Tokyo Inst. Tech (Prof.

Akiyama) Riken Genome Med. Inst. (Md.

and Dr Kamatani)

y q

network

Akiyama)

Estimation of large-scale protein network and its

applications and Dr. Kamatani)

Development for associating polymorphic data and phenotype

data and its validation applications

data and its validation

(23)

Attempt to realize personalization technique

Making a parallel computation scale larger enables us to carry out a data-dependent simulation, and results in drawing a scenario data dependent simulation, and results in drawing a scenario

and in making a risk assessment.

Prior distributionof Prior and posterior distributions for Prior distributionof

parameters

قleft؟10^5 right: 10^8ك Prior and posterior distributions for

three parameters among

parameters estimated PF are demonstrated in 3-dimensional space.

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10^5 particles results in the PDF with a small number of particles, the PF ith 10^8 particles

Posterior distributionof parameters PF with 10^8 particles

leaves many particles.

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Posterior distributionof parameters

Perspective of our Project

ũŞŪ

1. We automate a procedure searching for better simulation model to describe real phenomena.

2. We develop a procedure to generate a new simulation model that has greater ability of predictive performance than existing ones.

3. We give consistent view to assessment of simulation model that is said to be subsidiary problem in simulation science; Maximum

Lik lih d P i i l Likelihood Principle.

4. We give a platform to design a measurement system in an attempt

to enhance a scientific return together with reducing a total budgetary

cost.

Sequential Data Assimilation: