Title: Tensor methods for molecular dynamics simulations
Summary: In the beginning of the talk, an introduction to some tensor methods for the resolution of high-dimensional problems will be presented. A prototypical example of interest is the resolution of a Poisson problem with homogeneous boundary conditions in high dimension. I will present how tensor methods, in particular the so-called Proper Generalized Decomposition method, can be applied to compute approximations of the solution of such problems while circumventing the curse of dimensionality. The rest of the talk will then be focused on the presentation some recent developments in molecular dynamics simulations based on such tensor methods. The principles and objectives of molecular dynamics simulations will be recalled, with a particular emphasis to the so-called “metastability problem”. I will then present theoretical and numerical results about a new numerical method to circumvent this metastability problem, which relies in the adaptation of the so-called “Adaptive Biasing Force Method”
in the case where the number of reaction coordinates of the considered system is large. I will explain how this method can be combined with tensor approximations to circumvent the curse of dimensionality, along with the convergence results which can be proved for the resulting algorithm.
