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Workshop on Data Assimilation in the Sciences: Focus on Geophysical and Neuroscience Applications
WORKSHOP ON DATA ASSIMILATION IN THE SCIENCES：
FOCUS ON GEOPHYSICAL AND NEUROSCIENCE
APPLICATIONS
March 23- 26, 2015, Fudan University, Shanghai, China
http://ccsb.fudan.edu.cn/wdas2015/
Workshop on Data Assimilation in the Sciences：Focus on Geophysical and Neuroscience Applications
1
Workshop on Data Assimilation in the Sciences：Focus on Geophysical and Neuroscience Applications
Workshop on Data Assimilation in the Sciences：
Focus on Geophysical and Neuroscience Applications
Sponsored by
Centre for Computational Systems Biology, Fudan University
Shanghai Centre for Mathematical Sciences
Organized by
Centre for Computational Systems Biology, Fudan University
Shanghai Centre for Mathematical Sciences
Supported by
School of Mathematical Sciences, Fudan University
Workshop on Data Assimilation in the Sciences：Focus on Geophysical and Neuroscience Applications
LOCAL ORGANIZING COMMITTEE
General Chairs:
Andrew Stuart, Warwick University, UK
Henry Abarbanel, University of California, USA
Jianfeng Feng, Fudan University, P.R. China & Warwick University, UK
Co-chairs:
Wenlian Lu, Fudan University, P.R. China
Secretary:
Qianyi Zhang, Fudan University, P.R. China
Haiqing Wang, Fudan University, P.R. China
Workshop on Data Assimilation in the Sciences：Focus on Geophysical and Neuroscience Applications
CONTENTS
I.
TECHNICAL PROGRAM
…………………………………………… 1
March 23 ………………………………………………………………… 1
March 24 ………………………………………………………………… 2
March 25 ………………………………………………………………… 3
March 26 ………………………………………………………………… 4
II. CONFERENCE INFORMATION
R E G IS T R AT IO N
……………………………………5
………………………………………………………5
AC C O M M OD AT IO N …… …… …… ………… …… ……… ………… … 5
VENUE
…………………………………………………………………5
RECEPTION BANQUET
………………………………………………5
MEALS ………………………………………………………………5
TRANSPORTATION
……………………………………………….……6
CONTACTS ………………………………………………..…………..…………8
III. ABSTRACT
…………………………………………………….………9
IV. OVERVIEW OF CCSB
……………………………………………………26
Workshop on Data Assimilation in the Sciences: Focus on Geophysical and Neuroscience Applications
I. TECHNICAL PROGRAM
March 23, Monday
(Room 1801, East Guanghua Building, Fudan University)
Morning Session Panel（9:00–12:00）
Chair: Henry Abarbanel
9:00-9:30
Open Speech
Henry Abarbanel (University of California, San Diego)
9:30-10:30
Title: Data Assimilation: A coupling of Measures Perspective
Sebastian Reich (University of Potsdam)
10:30-11:00
Conference Photograph & Coffee Break
11:00-12:00
Title: A Low-order Coupled Chemistry Meteorology Model for
Testing Advanced Data Assimilation Schemes
Marc Bocquet ( École des Ponts ParisTech )
Afternoon Session (14:00-17:30)
Chair: Andrew Stuart
14:00-15:00
Title: Sampling Hazards in Data Inference
David Cai(New York University & Shanghai Jiao Tong University)
15:00-15:30
Coffee Break
15:30-16:30
Title: Data Based Modelling: Inferring Direct Directed Interactions
from Time Series
Bjoern Schelter (University of Aberdeen)
16:30-17:30
Title: Ensemble Bayesian Filtering in Oceanography: Successes
and Remaining Challenges
Ibrahim Hoteit (King Abdullah University of Science and
Technology)
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Workshop on Data Assimilation in the Sciences: Focus on Geophysical and Neuroscience Applications
March 24, Tuesday
(Room 1801, East Guanghua Building, Fudan University)
Morning Session (9:00-11:30)
Chair: Henk Nijmeijer
9:00-10:00
Title: Bayesian Inference for Markov Processes with Application
to Biochemical Network Dynamics
Darren Wilkinson (Newcastle University)
10:00-10:30
Coffee Break
10:30-11:30
Title: From Computational Neuronal Network to Functional MRI:
A Prospective of Data Assimilation
Wenlian Lu (Fudan University)
Afternoon Session (14:00-17:30)
Chair: Darren Wilkinson
14:00-15:00
Title: Synchronization in Networks of Diffusively (Time-delayed)
Coupled Semi-passive Systems: Does the Electronic Brain
Synchronize?
Henk Nijmeijer (Eindhoven University of Technology)
15:00-15:30
Coffee Break
15:30-16:30
16:30-17:30
Title: Intelligent Sensing, Data Analysis, and Health Monitoring
for Engineered and Biological Systems
Liming W. Salvino (US Office of Naval Research Global)
Title: Data Processing and Data Driven Modelling in Mental
Disorders
Jianfeng Feng (Fudan University & Warwick University)
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Workshop on Data Assimilation in the Sciences: Focus on Geophysical and Neuroscience Applications
March 25, Wednesday
(Room 2001, East Guanghua Building, Fudan University)
Morning Session (9:00-11:30)
Chair: Yuguo Yu
9:00-10:00
Title: In Silico Neuroscience: Emergent Structural and
Functional Properties of a Neocortical Microcircuit
Sean Hill (École Polytechnique Fédérale de Lausanne)
10:00-10:30
Coffee Break
10:30-11:30
Title: Implicit Sampling for Data Assimilation
Xuemin Tu (University of Kanas)
Afternoon Session (14:00-17:30)
Chair: Sean Hill
14:00-15:00
Title: Reconstructing Brain Energy Map and Conserved Energy
Budget Rules in Brain Gray Matter and White Matter Across
Species
Yuguo Yu (Fudan University)
15:00-15:30
Coffee Break
15:30-16:30
Title: On Ensemble and Particle Filters for Large-scale Data
Assimilation
Roland Potthast (Deutscher Wetterdienst and Reading
University)
16:30-17:30
Title: Filtering Partially Observed Chaotic Deterministic
Dynamical Systems
Andrew Stuart (Warwick University)
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Workshop on Data Assimilation in the Sciences: Focus on Geophysical and Neuroscience Applications
March 26, Thursday
(Room 2001, East Guanghua Building, Fudan University)
Morning Session (9:00-11:45)
Chair: Jianfeng Feng
9:00-10:00
Title: Defining Optimization Problems for Climate Study
Nozomi Sugiura (Japan Agency for Marine-Earth Science and
Technology )
10:00-10:30
Coffee Break
10:30-11:30
11:30-11:45
Title: TBA
Henry Abarbanel (University of California)
Close Talk
Andrew Stuart (Warwick University)
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Workshop on Data Assimilation in the Sciences: Focus on Geophysical and Neuroscience Applications
II. CONFERENCE INFORMATION
REGISTRATION
Could all participants please register at the earliest opportunity.
The registration desk will be open at the Lobby of Crowne Plaza Shanghai Fudan, 199
Handan Road (Near: Guoquan Road), on Sunday March 22nd from 13:30 – 17:30.
There will also be an opportunity to register at Room 1801, East Guanghua Building,
Fudan University, on Monday March 23rd from 08:30-09:00. Your conference
materials await collection at the Conference Registration Desk.
ACCOMMODATION
Accommodation will be arranged at Crowne Plaza Shanghai Fudan. It is located near
the main campus of Fudan University, which holds the conference venue.
VENUE
From March 23rd to March 24th, our conference will take place at Room 1801, East
Guanghua Building, which is located in the Handan Campus of Fudan University, 220
Handan Road, Shanghai, P.R.China. From March 25th to March 26th, our conference
will take place at Room 2001, East Guanghua Building, Fudan University.
RECEPTION BANQUET
The reception banquet will take place in the Chancellors Club on the 19th floor of
Crowne Plaza Shanghai Fudan, on Sunday March 22nd from 18:00 – 20:00.
MEALS
Lunches and Dinners from March 23rd to 26th will be provided to all participants on
the third floor of Danyuan Restaurant. Breakfast will be available in the hotel where
you are staying.
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Workshop on Data Assimilation in the Sciences: Focus on Geophysical and Neuroscience Applications
TRANSPORTATION
HOW TO REACH THE VENUE
From Airport To Fudan University (Handan Campus):
Hongqiao Airport:
1. Taxi to Fudan University costs roughly RMB 90.
2. Take a Metro Line 10 to Jiangwan Stadium Stop (江湾体育场站), which costs RMB 7, and
then walk (approximately 15 minutes to the Centre).
Pudong International Airport：
1. Taxi to Fudan University costs roughly RMB 160.
2. Shuttle Bus Line 4 (机场四线) to Wu Jiao Chang Stop (五角场) , which costs RMB 20, and
then walk (approximately 15 minutes to the Centre).
From Train Station To Fudan University (Handan Campus):
Shanghai Railway Station:
1. Get out from the South Exit of the Railway Station and then take a taxi to Fudan
University, which costs roughly RMB 30.
2. Get out from the North Exit of the Railway Station and then take a No. 942 Bus to Fudan
University Stop (复旦大学).
Shanghai South Railway Station:
Take a Metro Line 3 to Chifeng Road Stop (赤峰路) and then transfer to No. 139 or 854 or 942 or
991 Bus to Fudan University Stop (复旦大学).
Hongqiao Railway Station:
Take a Metro Line 10 to Jiangwan Stadium Stop (江湾体育场站), which costs RMB 7, and then
walk (approximately 15 minutes to the Centre).
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Workshop on Data Assimilation in the Sciences: Focus on Geophysical and Neuroscience Applications
Please show the following poster to the taxi driver, if you arrive at Shanghai and
intend to take a taxi at the airport or at the railway station to Crowne Plaza Shanghai
Fudan.
Please take me to: Crowne Plaza Shanghai Fudan
Address: 199 Handan Road (Near: Guoquan Road), Shanghai
Contact: 86-21- 55529999
请把我送到：
上海复旦皇冠假日酒店
地址：上海市邯郸路 199 号（国权路口）
联系电话: 86-21-55529999
Map of Fudan
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Workshop on Data Assimilation in the Sciences: Focus on Geophysical and Neuroscience Applications
CONTACTS
Wenlian Lu, Professor
Centre for Computational Systems Biology,
School of Mathematical Sciences,
Fudan University, Shanghai 200433, China
Contact Phone Number: +86-21-5566-5141
Email: wenlian@fudan.edu.cn
Qianyi Zhang, Secretary
Centre for Computational Systems Biology,
Fudan University, Shanghai 200433, China
Contact Phone Number: +86-21-5566-5546 ext. 8001
Email: zqy@fudan.edu.cn
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Workshop on Data Assimilation in the Sciences: Focus on Geophysical and Neuroscience Applications
Data Assimilation: A coupling of Measures Perspective
Sebastian Reich
University of Potsdam, Germany
sreich@math.uni-potsdam.de
Reliable forecasting requires the fusion of scientific modeling with available data.
When dynamkical phenomena are to be forecasted, this task leads to sequential data
assimilation problems which are best tackled from a Bayesian perspective.
Bayes' formula provides the centerpiece for Bayesian data assimilation and Bayesian
learning in general. However, beyond its conceptional simplicity and beauty, Bayes'
formula is hardly ever directly applicable and this is true in particular when Bayes'
formula needs to be interfaced with complex scientific models. In this context it is
better to talk of simulating Bayes' formula. Bayes' formula can be simulated in the
setting of sequential Monte Carlo methods and general Markov chain Monte Carlo
methods. However, those methods suffer from the curse of dimensionality.
In my talk, I will approach Bayes' formula from the perspective of coupling
probability measures and optimal transportation. This approach (i) naturally puts the
popular ensemble Kalman filters into context and suggests natural extensions to
non-Gaussian data assimilation problems, (ii) allows for the implementation of
sequential Monte Carlo methods in high dimensions using the concept of localisation,
and (iii) can be combined with quasi-Monte Carlo sampling approaches.
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Workshop on Data Assimilation in the Sciences: Focus on Geophysical and Neuroscience Applications
A Low-order Coupled Chemistry Meteorology Model for Testing
Advanced Data Assimilation Schemes
Marc Bocquet , Jean-Matthieu Haussaire
CEREA joint laboratory Ecole des Ponts ParisTech and EdF R&D,
Université Paris-Est, France.
bocquet@cerea.enpc.fr
In this talk I will illustrate the interest of developing a low-order model to test the
performance of advanced data assimilation schemes, as well as their feasibility to
higher dimensional models.
We have recently introduced a low-order model based on the coupling of the chaotic
Lorenz-95 model which simulates winds along a mid-latitude circle, with the transport
of a tracer species advected by this wind field. It has been used to test advanced data
assimilation methods with an online model that couples meteorology and tracer
transport. In the present study, the tracer subsystem of the model is replaced with a
reduced photochemistry module meant to emulate reactive air pollution. This coupled
chemistry meteorology model, the L95-GRS model, mimics continental and
transcontinental transport and photochemistry of ozone, volatile organic compounds
and nitrogen dioxides.
The L95-GRS is specially useful in testing advanced data assimilation schemes, such
as the iterative ensemble Kalman smoother (IEnKS) that combines the best of
ensemble and variational methods. The model provides useful insights prior to any
implementation of the data assimilation method on larger models. For instance, online
and offline data assimilation strategies based on the ensemble Kalman filter or the
IEnKS can easily be compared with it. It allows to document the impact of species
concentration observations on the wind estimation. The model also illustrates a long
standing issue in atmospheric chemistry forecasting: the impact of the wind chaotic
dynamics and of the chemical species non-chaotic but highly nonlinear dynamics on
the selected data assimilation approach.
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Workshop on Data Assimilation in the Sciences: Focus on Geophysical and Neuroscience Applications
Sampling Hazards in Data Inference
David Cai
New York University & Shanghai Jiao Tong University, P.R. China
cai@cims.nyu.edu
Erroneous inferences can arise in data processing due to sampling hazards. Their
resolutions often require one to go deeper to understand underlying dynamical
mechanisms. Two illustrative examples will be presented. The first example is
potential inference hazards in the application of Grange causality (GC). An effective
strategy of overcoming GC sampling issues will be described. In particular, the
detailed underlying mechanism for its successful application in the reconstruction of
the network topology of nonlinear neuronal networks will be discussed. The second
example will illustrate in detail how a large scale computational modeling of the
primary visual cortex (V1) has helped to resolve uncertainties about cortical
mechanisms inferred from optical imaging of the spatiotemporal dynamics of V1.
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Workshop on Data Assimilation in the Sciences: Focus on Geophysical and Neuroscience Applications
Data Based Modelling: Inferring Direct Directed Interactions
from Time Series
Bjoern Schelter
University of Aberdeen, UK
b.schelter@abdn.ac.uk
Recent years have seen a large increase in the availability of data. In fact, increasing
amounts of data play a key role in every aspect of our lives, including but not
restricted to physics, such as for the Large Hadron Collider (CERN) and the Square
Kilometre Array (South Africa), biology, e.g. genomic data, medicine, e.g. functional
magnetic resonance imaging or electroencephalography, and data mining in the social
sciences or digital economies.
Dealing with these data sets efficiently determines the success of the projects,
treatments, assessments, and analyses. This necessity to better understand and analyse
data has led to an outburst of research into advanced methods of data analysis. The
inference of networks underlying complex systems is of utmost importance.
Especially when dealing with complex data sets the algorithms for network inference
have to fulfil certain fundamental requirements: (i) they need to deal with truly
multivariate data, i.e. they must distinguish between direct and indirect influences, (ii)
they have to account for various concurrent noise sources, (iii) they need to addresses
both linear and non-linear systems, (iv) provide results for each sampling point, (v)
and estimate the strengths of the directed interactions. Finally, (vi) they need to
provide a rigorous statistical framework to allow their evaluation and (vii) be
numerically efficient.
A multitude of algorithms has been developed to address these extremely challenging
requirements, but until now only very few can address them simultaneously. This is
partly due to the fact that a rigorous mathematical framework, i.e. a theory of a
suitable highly versatile class of mathematical models to comprise all of these features,
is challenging. In this lecture, the challenges will be introduced and means to address
these will be discussed. Various methods will be compared and their abilities and
limitations will be discussed. This results in a comprehensive overview of techniques
that exists to tackle one of the key challenges of data based modelling: The detection
of direct directed interactions from time series.
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Workshop on Data Assimilation in the Sciences: Focus on Geophysical and Neuroscience Applications
Ensemble Bayesian Filtering in Oceanography:
Successes and Remaining Challenges
Ibrahim Hoteit
King Abdullah University of Science and Technology, Saudi Arabia
ibrahim.hoteit@kaust.edu.sa
Ensemble Kalman filters (EnKFs) have made long way since they have been
introduced for ocean data assimilation in the last decade, reaching performances
comparable to 4DVAR while offering computational flexibility and providing, even
crudely, estimates of uncertainties. In the first part of my talk I will present the EnKFs
and 4DVAR from a Bayesian formulation point of view, arguing that both are
different solutions for the same problem. I will present experiments results comparing
an EnKF and 4DVAR for predicting the evolution of the loop current in the Gulf of
Mexico. The second part of the talk will discuss the remaining challenges of the
EnKFs, focusing on the prior (or background) limitations and the Gaussian-based
analysis step. I will present an adaptive EnKF-Variational scheme that we have
introduced to mitigate the EnKF prior limitations and discuss its relation with the
hybrid EnKF-3DVAR schemes. I will also discuss recent developments for deriving
efficient non-Gaussian update schemes based on the Particle and Gaussian-Mixture
filters, or a hybrid scheme of these that we recently proposed.
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Workshop on Data Assimilation in the Sciences: Focus on Geophysical and Neuroscience Applications
Bayesian Inference for Markov Processes with Application to
Biochemical Network Dynamics
Darren Wilkinson
Newcastle University, UK
darren.wilkinson@ncl.ac.uk
A number of interesting statistical applications require the estimation of parameters
underlying a nonlinear multivariate continuous time Markov process model, using
partial and noisy discrete time observations of the system state. Bayesian inference for
this problem is difficult due to the fact that the discrete time transition density of the
Markov process is typically intractable and computationally intensive to approximate.
It turns out to be possible to develop particle MCMC algorithms which are exact,
provided that one can simulate exact realisations of the process forwards in time. Such
algorithms, often termed "likelihood free" or "plug-and-play" are very attractive, as
they allow separation of the problem of model development and simulation
implementation from the development of inferential algorithms. Such techniques
break down in the case of perfect observation or high-dimensional data, but more
efficient algorithms can be developed if one is prepared to deviate from the likelihood
free paradigm. The methods will be illustrated using examples from population
dynamics and stochastic biochemical network dynamics.
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Workshop on Data Assimilation in the Sciences: Focus on Geophysical and Neuroscience Applications
From Computational Neuronal Network to Functional MRI:
A Prospective of Data Assimilation
Wenlian Lu
Fudan University, P.R. China
wenlian@fudan.edu.cn
Functional MRI, known as BOLD signals, are indirect measurements of the neural
activities and so less capable to identify the variants of the neural system, in terms of
neurotransmitter receptors. An integration of fMRI analysis and computational
neuronal network model may enlighten the relationship between the characteristic
identified by fMRI study and the variants of the underlying neuronal network. To
conduct inference from BOLD signals to neuronal network model, data assimilation
might present an efficient method towards understanding the neurophysiological basis
of fMRI data.
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Workshop on Data Assimilation in the Sciences: Focus on Geophysical and Neuroscience Applications
Synchronization in Networks of Diffusively (Time-delayed) Coupled
Semi-passive Systems: Does the Electronic Brain Synchronize?
Henk Nijmeijer
Eindhoven University of Technology, Netherlands
h.nijmeijer@tue.nl
The talk consists of three parts.
In the first part of the talk we will discuss synchronization in a network of
semi-passive systems, i.e. systems that remain bounded if no external activation
occurs. The coupling is allowed to contain time-delay and thus mimics the fact that in
many physical and biological systems interaction does take some time. The results are
illustrated with numerical simulations.
In the second part we review shortly some basic mathematical properties that are valid
for all existing models of neuronal cells-at least as regarding their electrical activity.
We show that under fairly general conditions a network of neuronal cells will exhibit
synchronization provided their coupling structure is sufficiently strong. This result,
though often accepted, can be proven using the concept of semi-passivity. Next,
experimental results regarding an electronic realization of a network of neuronal
Hindmarsh-Rose systems are presented. Some of these results illustrate the
aforementioned theory, whereas additional experiments deal with (partial)
synchronization of time-delayed coupled neuronal systems and induce a conjecture
regarding scaling in network synchronization under time-delayed coupling.
In the third and final part we review how one can derive sufficient conditions for
time-delayed coupled network synchronization on basis of such results for possible
smaller and simpler networks.
[1] E.Steur, I.Tyukin, H.Nijmeijer, 'Semi-passivity and synchronization of diffusively
coupled neuronal oscillators', Physica D 238, pp.2119-2128, (2009).
[2] E.Steur, H.Nijmeijer, Synchronization in networks of diffusively time-delay
coupled (semi-) passive systems, IEEE Transactions on Circuits and Systems, vol 58
(8), 2011.
[3] P.J.Neefs, E.Steur, H.Nijmeijer, Network complexity and synchronous
behavior-an experimental approach, Intern Journal of Neural Systems, vol.20,
pp.233-247, 2010.
[4] E.Steur, W.Michiels, H.Huijberts and H.Nijmeijer, ‘Networks of diffusively
time-delayed coupled systems: Conditions for synchronization and its relation to the
network topolgy’, Physica D, 277, pp.22-37, 2014.
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Workshop on Data Assimilation in the Sciences: Focus on Geophysical and Neuroscience Applications
Intelligent Sensing, Data Analysis, and Health Monitoring for
Engineered and Biological Systems
Liming W. Salvino
US Office of Naval Research Global
Embassy of the United States of America, Singapore
liming.w.salvino.civ@mail.mil
The ability to turn data into information, knowledge, and innovative products often
separates success from failure. This presentation provides an overview of structural
health monitoring (SHM) technologies and illustrates how SHM can be greatly
improved by creating better data analytical methods through an adaptive data analysis
approach. SHM is a multidisciplinary science and engineering field with many
applications, including those in bio-medical sciences. Understanding data representing
nonlinear and non-stationary systems is the key for a successful future SHM
implementation applied to intelligent engineered and biological systems.
This
presentation also gives an overview of the Office of Naval Research Global (ONRG)
and its international program tools. ONRG strives to find innovative research, enable
technology awareness, and enhance communication and international collaborations.
A few ongoing and future international and interdisciplinary collaboration programs
for developing SHM technologies and data science will be discussed.
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Workshop on Data Assimilation in the Sciences: Focus on Geophysical and Neuroscience Applications
Data Processing and Data Driven Modelling in Mental Disorders
Jianfeng Feng
Fudan University, P.R. China & Warwick University, UK
jianfeng64@gmail.com
With the accumulated huge data at different scales ranging from whole genome to
different behaviours , we are facing challenging problems both in processing and
modelling. In the talk, we will first review some of our recent progresses in dealing
with genomic, whole brain images, and symptoms for autistic patients and
schizophrenia patients. With the largest image data in these disorders, we are able to
isolate the key altered areas and hence help us to search for the roots of these
disorders. Using modelling approaches, we intend to explore the mechanisms of these
disorders and we will illustrate the current difficulties we have.
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Workshop on Data Assimilation in the Sciences: Focus on Geophysical and Neuroscience Applications
In Silico Neuroscience: Emergent Structural and Functional
Properties of a Neocortical Microcircuit
Sean Hill
École Polytechnique Fédérale de Lausane, Switzerland
sean.hill@epfl.ch
The Blue Brain Project consortium has developed a predictive, algorithmic
reconstruction strategy that integrates sparse experimental data to derive principles of
brain structure and function. A first draft detailed anatomical and physiological map
of a prototypical neocortical microcircuit will be presented. This approach integrates
knowledge and data from the literature and from experimental neuroscience including
single and multi-cell electrophysiology, morphological reconstruction, gene
expression, ion channel kinetics and in vitro network experiments using
multi-electrode arrays. The resulting model microcircuit is 0.28 mm3 in volume and
contains 31,000 neurons belonging to 55 morphological neuron types and 207
morpho-electrical sub-types distributed across 6 layers. The model predicts: the
number of neurons of each type per layer (the neurome) with around 7.5 million
intrinsic and 27 million extrinsic connections forming around 40 and 141 million
synapses, respectively (the connectome); the detailed anatomy and physiology of
2,258 unique synaptic pathways between neurons of different morphological types,
31,628 unique pathways between neurons of different morpho-electrical types, 600
intra- laminar and 1,658 inter-laminar pathways; and the complete map of intrinsic
synapses for all neurons (their synaptomes). In silico simulations of the reconstructed
microcircuit provide novel, simple and standardized measures of microcircuit
behaviour and the computational role of any component of the microcircuit.
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Workshop on Data Assimilation in the Sciences: Focus on Geophysical and Neuroscience Applications
Implicit Sampling for Data Assimilation
Xuemin Tu
The University of Kanas, USA
xtu@math.ku.edu,xuemin@ku.edu
Applications of filtering and data assimilation arise in engineering, geosciences,
weather forecasting, and many other areas where one has to make estimations or
predictions based on uncertain models supplemented by a stream of data with noise.
For nonlinear problems, filtering can be very expensive since the number of the
particles required can grow catastrophically. We will present a particle-based
nonlinear filtering scheme. This algorithm is based on implicit sampling, a new
sampling technique related to chainless Monte Carlo method. This sampling strategy
generates a particle (sample) beam which is focused towards on the high probability
region of the target pdf and the focusing makes the number of particles required
manageable even if the state dimension is large. Several examples will be given.
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Workshop on Data Assimilation in the Sciences: Focus on Geophysical and Neuroscience Applications
Reconstructing Brain Energy Map and Conserved Energy Budget
Rules in Brain Gray Matter and White Matter Across Species
Yuguo Yu
Fudan University, P.R. China
yuyuguo@fudan.edu.cn
The human brain is organized on multiple scale network connections and
function-dependent regions for low-level sensory information processing to
high-order cognitive functions. How is the metabolic energy distributed within the
brain supporting those activities is not known well. Are there any economic principles
and computational rules underlying brain energy distribution in normal/abnormal
brains? In this study, we first calculated energy consumptions in all the known brain
components (signaling and non-signaling) of brain cells (including GABAergic
interneurons, glutamate-based excitatory neurons, glia cells) in gray matter and white
matter based on existing physiological parameters of cells, spiking activities and
synaptic transmissions. We then confirmed these brain energy budget calculations
with functional MRI and 13C MRS measurements. We next calculated the cell
density distribution based on cluster analysis of the BigBrain data (a reconstruction of
7404 cell-stained histological Sections with cellular resolution of 20 micrometer, from
a donated 65-years old healthy woman brain, (2013, Science “BigBrain: An
Ultrahigh-Resolution 3D Human Brain Model”). Then, we feed the energy budget
calculations of individual neurons and glia into brain cell density map, formulating a
3-D brain energy map with energy calculations in unit of either glucose in
micromole/min/gram or ATP/min/gram in order to compare with PET measurement
of actual brain. The quantitative comparison demonstrated a perfect match, indicating
a successful first reconstruction of brain energy map fully consistent with PET
glucose imaging measurement. The results suggest: 1) the brain energy changes are
mainly controlled by a key factor, i.e., the mean firing rate. Resting human brain
might have an averaged firing rate ~1-1.5 Hz, as expected from previous experimental
evidences (~1 Hz for the human brain). 2) The brain energy distribution statistics are
majorly determined by the densities of neuronal and glia cell distributions. 3)
Bottom-up energy budget calculations can capture the major energy consumption
sources, which include contributions from housekeeping, resting potential, action
potentials, synaptic potentials for neurons and glia in both gray matter and white
matter. 4) Brain signaling processes consume over 62% of gray matter and 25% of
white matter energy; all cortical glia cells consume about 11% of gray matter energy;
all the GABAergic neurons consume 20% of whole energy for neuronal populations.
Most importantly, these percentage rules are same for both the human brain and rat,
suggesting general rules conserved across species for brain energy budget from
mammals, primates to humans.
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Workshop on Data Assimilation in the Sciences: Focus on Geophysical and Neuroscience Applications
On Ensemble and Particle Filters for Large-scale Data Assimilation
Roland Potthast
Deutscher Wetterdienst, Germany & Reading University, UK
Roland.Potthast@dwd.de
In almost all operational centres for numerical weather prediction around the world
ensemble data assimilation techniques are of rapidly growing importance. Ensemble
techniques allow to describe and forecast uncertainty of the analysis, but they also
improve the assimilation result itself, by allowing estimates of the covariance or, more
general, the prior and posterior probability distribution of atmospheric states.
In our talk, we will first give a survey about recent activities of the German
Meteorological Service DWD, who is working towards the use of an Ensemble
Kalman Filter both for its new global ICON model as well as for the convective scale
high-resolution model COSMO-DE. To be more precise, for the global model a
hybrid variational ensemble Kalman filter (VarEnKF) is under development. We
survey the setup of its Ensemble Kalman Filter component, which is based on the
LETKF of Hunt, with a range of further features such as relaxation to prior
perturbations or random perturbations. Then, for the kilometer scale ensemble data
assimilation (KENDA) for the 2.8km/2.2km resolution COSMO-DE model we
des-cribe the ensemble Kalman filter which is being tuned for operational use and
show recent results which demonstrate that it is clearly superior to the current nudging
scheme. We will also point to very encouraging results on the performance of the
COSMO-DE-EPS when initial conditions for its 40-member ensemble are taken from
KENDA.
In collaborations with several universities and the DWD-funded Hans Ertel Centre on
Weather Research (HErZ), research groups employ the ensemble Kalman filter of
KENDA as a basis for further research on the assimilation of particular observation
systems, such as radar reflectivities, MODE-S data or SEVIRI radiances. We give a
brief survey about the state of these projects.
In the third part of the talk, we present recent work on the further development of the
ensemble data assimilation towards a particle filter for large-scale atmospheric
systems, which keeps the advantages of the LETKF, but overcomes some of its
limitations. We describe a Localized Markov Chain Particle Filter (LMCPF), present
its mathematical foundation and show some tests for simple systems. The
implementation of the LMCPF in the KENDA framework of DWD is ongoing work.
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Workshop on Data Assimilation in the Sciences: Focus on Geophysical and Neuroscience Applications
Filtering Partially Observed Chaotic Deterministic
Dynamical Systems
Andrew Stuart
Warwick University, UK
andrewmstuart@gmail.com
This talk is concerned with determining the state of a chaotic dynamical system, for
which the initial condition is only known probabilisticlly, given partial and noisy
observations. In particular it is of interest to study this problem in the limit of a large
number of such observations, over a long time interval. A key question is to determine
which observations are sufficient in order to accurately recover the signal, and thereby
overcome the lack of predictiability caused by sensitive dependence on initial
conditions. A canonical application is the development of probabilistic weather
forecasts.
The evolution of many physical systems can be successfully modelled by a
deterministic dynamical system for which, however, the initial conditions may contain
uncertainty. In the presence of chaos this can lead to undesirable growth of
uncertainty over time. However, when noisy observations of the system are present
these may be used to compensate for the uncertainty in the initial state. This
scenario is naturally modelled by viewing the initial state as given by a probability
distribution, and to then condition this probability distribution on the noisy
observations, thereby reducing uncertainty. This reduced uncertainty on the initial
condition results in reduced uncertainty on the system state at later times. Filtering
refers to the situation where the conditional distribution on the system state is updated
sequentially, at the time of each observation. The objective of the work described in
this talk is to study the asymptotic behaviour of this filtering distribution for large
time, a question which relates to the issue of predictability in noisily observed chaotic
dynamical systems.
In order to study this problem concretely, we will focus on a wide class of dissipative
differential equations with quadratic energy-conserving nonlinearity, including the
Lorenz 63 and Lorenz 96 models, as well as the Navier-Stokes equation on a 2D torus.
The talk will combine ideas from control theory (nonlinear observer), dynamical
systems (synchronization) and probability (optimal filter and Galerkin orthogonality)
to provide concrete results for this wide class of models. Furthermore, we will
consider continuous time limits of the algorithms which give rise to various
interesting stochastic partial differential equations (SPDEs). The techniques used to
prove our results will build upon two algorithms that are widely used in the numerical
weather prediction community, namely the 3DVAR and Ensemble Kalman Filter
(EnKF) methods.
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Workshop on Data Assimilation in the Sciences: Focus on Geophysical and Neuroscience Applications
The synchronization techniques which underlie this work are developed in [1] and
prototypical results concerning nonlinear observers may be found in [2]. The
probabilistic results in this talk, which build on the work in [1,2], may be found in [3].
Further background in the 3DVAR and EnKF methods, as well as derivation of their
continuous time SPDE limits, may be found in [4,5,6]. The book [7] provides a
pedagogical introduction to this material.
[1] K. Hayden, E. Olsen and E.S. Titi, “Discrete data assimilation in the Lorenz and
2D Navier?“Stokes equations.'' Physica D 240(2011) 1416-1425.
[2] T. Tarn and Y. Rasis, “Observers for nonlinear stochastic systems''. IEEE
Transactions on Automatic Control 21(1976) 441--448.
[3] D. Sanz-Alonso and A.M.Stuart, “Long-time asymptotics of the filtering
distribution for partially observed chaotic deterministic dynamical systems.''
http://arxiv.org/abs/1411.6510
[4] K.J.H. Law, A. Shukla and A.M. Stuart, “Analysis of the 3DVAR filter for the
partially observed Lorenz '63 model.'' Discrete and Continuous Dynamical Systems A,
34(2014), 1061-1078. http://arxiv.org/abs/1212.4923
[5] D. Bloemker, K.J.H. Law, A.M. Stuart and K. Zygalalkis.”Accuracy and stability
of the continuous-time 3DVAR filter for the Navier-Stokes equation”. Nonlinearity
26(2013), 2193-2219. http://arxiv.org/abs/1210.1594
[6] D.T.B. Kelly and K.J.H. Law and A.M. Stuart. “Well-posedness and accuracy of
the ensemble Kalman filter in discrete and continuous time”. Nonlinearity 27(2014),
2579-2603. http://arxiv.org/abs/1310.3167
[7] K.J.H. Law, A.M.Stuart and K. Zygalalkis, “Data Assimilation: A Mathematical
Introduction.” In preparation, 2015.
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Workshop on Data Assimilation in the Sciences: Focus on Geophysical and Neuroscience Applications
Defining Optimization Problems for Climate Study
Nozomi Sugiura
Japan Agency for Marine-Earth Science and Technology, Japan
nsugiura@jamstec.go.jp
To make climate data assimilation problems tractable, we usually change the
optimization problem into a regularized form.
The regularization is realized by attracting rapid modes to a reference model field.
Also, I will discuss about how to formulate an effective cost function for climate
study.
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Workshop on Data Assimilation in the Sciences: Focus on Geophysical and Neuroscience Applications
IV. OVERVIEW OF CCSB
The Centre for Computational Systems Biology (CCSB) of Fudan University was
founded in March 2008. Our center focuses its research on Computational
Neuroscience/Biology and Cellular Biology. The director of the centre is Professor
Jianfeng Feng, also professor and head of the Laboratory of Computational Biology in
Warwick University, United Kingdom.
The Centre now has around thirty+ research members, an administrative assistant, two
research assistants, and twenty+ Ph.D. students. The Centre is divided into three
Research Groups, Cellular Biology, Computational Neuroscience, and Computational
Biology.
The members of the centre have various academic backgrounds, ranging from applied
mathematics to statistics, from biology physics to molecular biology, and to
neuroscience. We have published papers in
Nature (6),
Science (7),
Mol. Psychiatry (1)
Curr. Biol. (3),
PNAS (5),
Mol. Sys. Biol. (1),
J. Neurosci. (4),
PRL (5),
PLoS Comp. Biol. (7)
and others.
The Centre is currently in a growing phase. We welcome applications from colleagues
interested in joining us.
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