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MEthodes Géométriques et échantillonnage: Application à la Simulation moléculaire – MEGAS

Submission summary

Today's and tomorrow's materials are developed at a microscopic level, using information at ever smaller time and space scales. In many cases, these materials are described at the atomic level, based upon the physical theories of quantum physics and statistical physics. Molecular simulation aims at numerically investigating the physical properties of materials, and is employed in the fields of materials science, chemistry, biophysics, nuclear energy, etc. This field, in essence, an interdisciplinary domain, calling for contributions from many mathematical communities (covering the whole spectrum from partial differential equations (PDEs) and probability theories, to numerical analysis and scientific computing), and in connection with many applicative domains. There is a need to establish a solid expertise in France covering all the mathematical and numerical aspects required in the study of molecular simulation algorithms. The ANR already contributed to the development of such an expertise through the ANR project INGEMOL, which ended this year. The ANR project MEGAS is a follow-up to the INGEMOL project, with new directions of research concerning stochastic methods. The acceptance of this project would greatly contribute to the development of these research themes in France. The main focus of this proposal is to further study the numerical methods used in molecular simulation, insisting on the preservation of structural properties of the underlying models, in the context of deterministic or stochastic dynamics, and for equilibrium or nonequilibrium problems. We believe our team is well-suited to this end since it is composed of applied mathematicians specialized in Hamiltonian dynamics, probability theory and numerical analysis, as well as scientists closer to the applications, either applied mathematicians working with physicists, chemists, etc, as well as a researcher in computational biology. Therefore, the skills range from the theoretical study of the models to the practical implementation and validation of the proposed algorithms on test cases relevant to some applied communities. More precisely, our team consists of four partners: the molecular and multiscale modeling group at Ecole des Ponts (partner 1), the IPSO team-project at INRIA Rennes (partner 2), Mathias Rousset at INRIA Lille (partner 3) and Chris Chipot at CNRS Nancy (partner 4). These partners have complementary skills which are relevant to this project. Partner 1 has developed a good understanding of the models used by practitioners, and has a wide spectrum of expertise, ranging from the stochastic analysis to the analysis of PDEs, including numerical analysis of stochastic and deterministic methods. Partner 2 is specialized in deterministic methods in molecular dynamics, with an emphasis on geometric integrators for Hamiltonian systems. The focus of Partner 3 is Monte Carlo methods, and more precisely, particle methods, which are widely used in molecular dynamics simulations. Finally, Partner 4 is directly involved in large scale computations for biological applications. His role in this project is both to ensure the practical significance of the questions addressed by the mathematical participants, and to test the interest of the new strategies proposed on real test cases. We intend to focus our efforts on some current 'hot topics' in the domain, which define the six tasks of the project: (1) computation of free energy differences and improved sampling, (2) highly oscillating dynamics, (3) coarse-graining of dynamics, (4) steady state nonequilibrium sampling, (5) Quantum Monte-Carlo, (6) discrete to continuum coupling methods. Some of the new theoretical results and numerical methods obtained in this project will benefit from an implementation in existing industrial or academic codes, and so, may be used directly by applied communities. Moreover, we intend to organize a summer school in France in the academic year 2009-2010 in order to advertise the topic to our fellow French colleagues, and to stimulate collaborations with foreign teams working on the subject. To conduct this ANR project, we ask for two one-year postdoctoral positions, one three-year PhD position, and some additional funding for equipment (computing resources), for the organization of the summer school and for participations to international conferences. One of the main aim of these missions is to attract post-doctoral students, whose hiring is exceedingly difficult in a highly competitive job market.

Project coordination

The author of this summary is the project coordinator, who is responsible for the content of this summary. The ANR declines any responsibility as for its contents.

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Beginning and duration of the scientific project: - 0 Months

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