It is well-known that the convergence of a Langevin process toward its equilibrium, which is needed for the computation of observables with respect to the Gibbs measure in molecular dynamics simulation, may be very slow. This is due to the so-called metastability phenomenon because of which the process remains for very long times in some regions of the state space, with very rare transitions from one of these metastable region to the other. For this reason, several adaptative methods have been developed in order to accelerate the convergence of such a stochastic process to its equilibrium measure, among which the Adaptive Biasing Force (ABF) algorithm. The ABF method relies heavily on the use of so-called reaction coordinates, which can be considered as reduced coordinates of the molecular system, and the computation of the free energy of the system, which can be seen as a function of the chosen reaction coordinates. However, when the number of reaction coordinates of interest is too large, standard algorithms for the computation of the cannot be afforded from a computational view. In this talk, a new version of the ABF method will be presented, where the free energy is approximated by a sum of tensor products of one-dimensional functions, thus avoiding the curse of dimensionality arising when the number of reaction coordinates is large. Theoretical and numerical results for this Tensorized ABF algorithm will be presented and discussed.
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