This talk will focus on the presentation some recent developments in molecular dynamics simulations based on 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. We prove the algorithm is well-defined and prove the long-time convergence toward a regularized version of the free energy for an idealized version of the algorithm. Numerical experiments demonstrate that the method is able to capture correlations between reaction coordinates.
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