DqF Workshop Stochastic Differential Equations: Models and Numerics Circumspect descent prevails in solving random con- straint satisfaction problems

One aim of molecular dynamics simulations is to sample Boltzmann-Gibbs measures associated to some potentials in high dimensional spaces, to compute macroscopic quantities (such as chemical reaction constants, or diffusions constants) by statistical means in the canonical (NVT) ensemble. Numerical methods typically rely on ergodic limits for processes solution to well-chosen stochastic differential equations (SDEs). The main difficulty comes from existence of metastable states in which the stochastic processes remain for long time: this may slow down dramatically the convergence of the ergodic limit. We present a class of adaptive importance sampling methods which enable fast exploration of the configurational space, by modifying the potential seen by the particles (the associated SDE becomes