Entrance hall of the ICMS Workshop

Stochastic Particle Methods, Maxwell Colloquium 4 - 6 February

Feb 04, 2015 - Feb 06, 2015

ICMS, 15 South College Street, Edinburgh

Organisers

Name Institution
Gibson, Gavin Heriot-Watt University
Szpruch, Lukasz University of Edinburgh

The main purpose of the colloquium is to gain insight into new developments of Stochastic Particle Methods, which include both linear and non-linear Monte Carlo type methods.  The colloquium on Friday 6 February will be preceded by a two-day mini-course on the afternoons of Wednesday 4 & Thursday 5 February on "Mean Field Simulations for Monte Carlo Integration" delivered by Pierre Del Moral. This is great opportunity to better understand fundamentals behind the theme of the colloquium and further induce synergies among members of Maxwell Institute. 

The colloquium and mini-course are open to all staff members  and postgraduate students of the University of Edinburgh and Heriot-Watt University.

Please register using this form.

The schedule for the mini-course and colloquium can be found below:

Keynote Speakers:

Pierre Del Moral

Pierre is a professor at the School of Mathematics and Statistics at the University of New South Wales, Sydney.  He is a world-class researcher in the field of Particle methods, Filtering, Sequential Monte Carlo and Mean Field approximations. He is one of the main developer of so called Particle Methods that are of increasing importance in simulations of a multidimensional complex system.  Pierre’s research is on both theoretical and abstract mathematics but he also blends his result with applications in many important research areas such as:  Propagations of chaos, Central limit theorems, Large deviation,  Filtering and multiple object tracking, Bayesian Inference, Financial Mathematics, Biology and Chemistry. He has authored 7 books (4 research monograph) and over 100 research publications (many of them in the top journals). He also was involved in an impressive number of academic and industrial research projects.

Benjamin Jourdain

Benjamin is a professor at Ecole Nationale des Ponts et Chaussées in Paris. He is a head of the Applied Probability team at CERMICS, Head of the École Doctorale MSTIC Université Paris-Est and a member if the INRIA project-team MathRisk.  He is renowned for his research on stochastic particle systems, Monte Carlo methods and  probabilistic interpretations of the equations arising in fluid dynamics.  His research interests are: Probabilistic numerical methods in finance and molecular simulation : discretization of SDEs, variance reduction, MCMC ; Risk modelling in finance; Optimal transport and longtime behaviour of Markov processes;  Probabilistic interpretation of nonlinear evolution equations as Fokker-Planck equations associated with stochastic processes; Approximation of these processes thanks to systems of interacting particles.

Preliminary Programme

All talks will take place at ICMS

Colloquium Friday 6 February:

10:20 - 10:30  Opening
10:30 - 11:00  Michela Ottobre (Heriot-Watt)
11:00 - 11:30  Burak Buke (University of Edinburgh)
11:30 - 12:00  Goncalo dos Reis (University of Edinburgh)
12:00 - 13:30  Lunch Break
13:30 - 14:30  Benjamin Jourdain (CERMICS)
14:30 - 15:30  Pierre Del Moral (UNSW)

Mini-Course 4-5 February

Mini-course will take place at ICMS.
Wednesday 4 February:
13.30 - 15:30 Pierre Del Moral
15:30 - 16:00  Coffee break
16:00 - 17:30 Pierre Del Moral

Thursday 5 February:
13.30 - 15:30 Pierre Del Moral
15:30 - 16:00  Coffee break
16:00 - 17:30 Pierre Del Moral

Titles and Abstracts

Pierre Del Moral

Title: An introduction to Feynman-Kac integration and genealogical tree based particle models.

Abstract: In the last three decades, there has been a dramatic increase in the use of particle methods as a powerful tool in real-world applications of Monte Carlo simulation in computational physics, population biology, computer sciences, and statistical machine learning. Ideally suited to parallel and distributed computation, these advanced particle algorithms include nonlinear interacting jump diffusions; quantum, diffusion, and resampled Monte Carlo methods; Feynman-Kac particle models; genetic and evolutionary algorithms; sequential Monte Carlo methods; adaptive and interacting Markov chain Monte Carlo models; bootstrapping methods; ensemble Kalman filters; and interacting particle filters. This lecture presents a comprehensive treatment of mean field particle simulation models and interdisciplinary research topics, including sequential Monte Carlo methodologies, genetic particle algorithms, genealogical tree-based algorithms, and quantum and diffusion Monte Carlo methods.


Benjamin Jourdain

Title: Multitype sticky particles and diagonal hyperbolic systems of PDEs.

Abstract: In dimension one, under the sticky dynamics, particles move with constant velocity between collisions and then stick together with conservation of the mass and momentum. According to Brenier and Grenier 1998, the large scale behaviour of this dynamics is given by the entropy solution to a scalar conservation law. Stability estimates in Wasserstein distance for such solutions was later proved by Bolley, Brenier and Loeper 2005.
We introduce a multitype version of the sticky particles dynamics where each particle has a type, only sticks with particles of the same type and undergoes a velocity change when colliding a particle with another type. Under a uniform strict hyperbolicity assumption saying that the ranges of velocities for each type are disjoint intervals, we prove that the large scale behaviour of this dynamics is given by weak solutions to a diagonal hyperbolic system of PDEs. We then derive a Lp stability estimate on the particle system uniform in the number of particles. This allows to construct a nonlinear semigroup solving the system in the sense of Bianchini and Bressan 2005 and stable in Wasserstein distances of all orders. (joint work with J. Reygner)

Goncalo dos Reis

Title: Customized numerical schemes for FBSDEs.

Abstract: In this talk we introduce a family of explicit numerical approximations for the forward backward stochastic differential equations (FBSDEs). We show that newly developed methodology allows to analyse BSDEs with drivers having polynomial growth and that are also monotone in the state variable. This offers a probabilistic scheme for wide class of reaction-diffusion PDEs. Proposed schemes preserve qualitative properties of the solutions to the FBSDEs for all ranges of time-steps. (joint work with A. Lionnet and L. Szpruch )

Burak Buke

Title: Monte Carlo Methods for Stochastic Optimization.

Abstract: Monte Carlo methods are used extensively for assessing the solution quality in stochastic programs. It is known that the using sample average approximations provide us with a biased estimator of the optimal objective value. In this talk, we will review the literature on applications of Monte Carlo simulation in Stochastic programming.  We also suggest a Monte Carlo method, which relies on estimating the objective value as a telescopic sum, and discuss how it helps us reduce the bias and variance in an efficient manner.

Michela Ottobre

Title: A Function Space HMC Algorithm with second order Langevin diffusion limit.

Abstract: We describe a new MCMC method optimized for the sampling of probability measures on Hilbert space which have a density with respect to a Gaussian; such measures arise in the Bayesian approach to inverse problems, and in conditioned diffusions. Our algorithm is based on two key design principles: (i) algorithms which are well-defined in in finite dimensions result in methods which do not suffer from the curse of dimensionality when they are applied to approximations of the in finite dimensional target measure on R^N; (ii) non-reversible algorithms can have better ergodic properties compared to their reversible counterparts. The method we introduce is based on the hybrid Monte Carlo algorithm, tailored to incorporate these two design principles. (joint work with N. Pillai, F. Pinski and A. Stuart)

 

Participants

Name Institution
Antal, Tibor University of Edinburgh
Azalekor, Abla Heriot-Watt University
Bahl, Raj University of Edinburgh
Barnes, Gwendolyn Heriot-Watt University
Branicki, Michal University of Edinburgh
Buke, Burak University of Edinburgh
Chen, Hanyi University of Edinburgh
Christiansen, Marcus Heriot-Watt University
Clancy, Damian Heriot-Watt University
Daniel, Tait University of Edinburgh
de Langlard, Mathieu University of Edinburgh
Dos Reis, Goncalo University of Edinburgh
Dreher, Michael Heriot-Watt University
Gavin, Gibson Heriot-Watt University
Gerencsér, Máté Institute of Science and Technology Austria
Konecny, Jakub University of Edinburgh
Kumar, Chaman University of Edinburgh
Leimkuhler, Benedict University of Edinburgh
Lionnet, Arnaud INRIA
Lord, Gabriel Heriot-Watt University
Miyazawa, Masakiyo Tokyo University of Science
Moraki, Eleni MIGSAA
Oh, Tadahiro University of Edinburgh
Ottobre, Michela Heriot-Watt University
Pollock, Jeffrey Heriot-Watt University
Rodriguez Villarreal, Jose Gregorio University of Edinburgh
Sabanis, Sotirios University of Edinburgh
Sachs, Matthias University of Edinburgh
Schmuck, Markus Heriot-Watt University
Shang, Xiaocheng University of Edinburgh
Siska, David University of Edinburgh
Smith, Greig University of Edinburgh
Szpruch, Lukasz University of Edinburgh
Tanner, Eleanor MIGSAA
Thong, David Heriot-Watt University
Tsardakas, Michael Heriot-Watt University
Wong, Ming Yi Heriot-Watt University
Zhang, Xiling University of Edinburgh