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math.AP2015
Local and global solution for a nonlocal Fokker-Planck equation related to the adaptive biaising force processes
Houssam Alrachid, Tony Lelièvre, Raafat Talhouk
We prove global existence, uniqueness and regularity of the mild, Lp and classical solution of a non-linear Fokker-Planck equation arising in an adaptive importance sampling method…
math.NA2015
Long-time convergence of an adaptive biasing force method: Variance reduction by Helmholtz projection
Houssam Alrachid, Tony Lelièvre
In this paper, we propose an improvement of the adaptive biasing force (ABF) method, by projecting the estimated mean force onto a gradient. The associated stochastic process satis…