COmputational Statistics and MOlecular Simulation – COSMOS

This proposal aims at developing numerical techniques dedicated to the sampling of high-dimensional probability measures describing a system of interest. There are two application fields of interest: computational statistical physics (a field also known as molecular simulation), and computational statistics. These two fields share some common history, but it seems that, in view of the quite recent specialization of the scientists and the techniques used in these respective fields, the communication between molecular simulation and computational statistics is not as intense as it should be.

We believe that there are therefore many opportunities in considering both fields at the same time: in particular, the adaption of a successful simulation technique from one field to the other requires first some abstraction process where the features specific to the original field of application are discarded and only the heart of the method is kept. Such a cross-fertilization is however only possible if the techniques developed in a specific field are sufficiently mature: this is why some fundamental studies specific to one of the application fields are still required. Our belief is that the embedding in a more general framework of specific developments in a given field will accelerate and facilitate the diffusion to the other field.

More specifically, we divided the scientific program in four main scientific tasks:
1) the analysis and development of adaptive sampling techniques from molecular simulation, which use estimates of the free energy updated on-the-fly to bias the dynamics in specific directions of low probability and reduce the metastability of the system. An important goal of this project is also to advertise such techniques for computational statistics;
2) the sampling of reactive trajectories linking two local maxima of the probability distribution of the system, using techniques from computational statistics based on the splitting paradigm, with extensions and modifications suggested by analogous methods in molecular simulation. We also aim at performing the numerical analysis of the method;
3) the study of Metropolis-Hastings algorithms, which are relevant both for molecular simulation and computational statistics. Two situations are of interest: (a) when the dynamics is off equilibrium, for instance at the beginning of the simulation, in the transient regime before the system is equilibrated, how should the magnitude of the proposal function be chosen? (b) when the proposal function is given by the discretization of some continuous stochastic differential equation, is it possible to modify the Metropolis-Hastings procedure in order to correctly approximate dynamical properties such as correlation functions?
4) the use of non-reversible perturbations of reversible, equilibrium dynamics to increase the exploration power and/or reduce the variance of the computations. Such modifications naturally appear in molecular simulation in some contexts.

The partners in the proposal have complementary skills related to the aims of the proposal: the researchers from Ecole des Ponts are applied mathematicians specialized in the study of numerical methods from molecular simulation, while the teams from Institut Mines-Telecom and Inria Rennes are computational statisticians. Finally, the presence of a theoretical biochemist developing numerical methods and running large scale biomolecular simulations ensures the relevance of the applications on the molecular simulation side.

To conduct this project, we ask for one PhD student position and a one-year post-doctoral fellowship, as well as some additional funding for travel expenses and computer equipment.