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Molecular Simulation: modeling, algorithms and mathematical analysis

Objective

Many models for materials rely on a microscopic description. In a classical regime and for a fixed temperature, atoms are described by particles that interact through a force field and evolve according to Newton’s equations of motion, with additional stochastic terms to model thermostating. This simulation technique is called molecular dynamics. Applications are ubiquitous, ranging from biology to materials science.

The direct numerical simulation of these models is extremely computationally expensive, since the typical timescale at the microscopic level is orders of magnitude smaller than the macroscopic timescales of interest. Many algorithms used by practitioners have not yet been investigated by applied mathematicians. The aim of this proposal is to further develop the mathematical analysis of these methods and to build new and more efficient algorithms, validated by precise error estimates.

The underlying theoretical questions are related to the mathematical definition and quantification of metastability for stochastic processes. Metastability refers to the fact that the stochastic process remains trapped in some regions of the configuration space for very long times. Using naive simulations, transitions between these states are very rarely observed, whereas these transition events are actually those which matter at the macroscopic level. Metastability is one of the major bottlenecks in making molecular simulations predictive for real life test cases.

The main challenges motivating this proposal are: the design of efficient techniques to sample high-dimensional multimodal measures, the development and analysis of algorithms to sample metastable dynamics and the construction of coarse-graining techniques for high-dimensional problems.

This project relies on strong collaborations with practitioners (biologists and physicists) in order to propose common benchmarks, to identify the methodological bottlenecks and to apply new algorithms to real life test cases.

Field of science

  • /natural sciences/mathematics/pure mathematics/mathematical analysis
  • /natural sciences/physical sciences/theoretical physics/particles

Call for proposal

ERC-2013-CoG
See other projects for this call

Funding Scheme

ERC-CG - ERC Consolidator Grants

Host institution

ECOLE NATIONALE DES PONTS ET CHAUSSEES
Address
Avenue Blaise Pascal-cite Descartes-champs-sur-marne 6-8
77455 Marne La Vallee Cedex 2
France
Activity type
Higher or Secondary Education Establishments
EU contribution
€ 1 773 600
Principal investigator
Tony Gilbert Lelievre (Prof.)
Administrative Contact
Carolina Garcia-Olmedo (Ms.)

Beneficiaries (1)

ECOLE NATIONALE DES PONTS ET CHAUSSEES
France
EU contribution
€ 1 773 600
Address
Avenue Blaise Pascal-cite Descartes-champs-sur-marne 6-8
77455 Marne La Vallee Cedex 2
Activity type
Higher or Secondary Education Establishments
Principal investigator
Tony Gilbert Lelievre (Prof.)
Administrative Contact
Carolina Garcia-Olmedo (Ms.)