I will present a family of Adaptive Biasing Potential algorithms, for diffusions processes, in continuous-time. I will insist on the mathematical structure, which encompasses many examples: overdamped Langevin and Langevin SDEs, parabolic SPDEs...

The algorithm is based on sampling a single trajectory of the stochastic dynamics, whose coefficients depend on the past (self-interacting diffusion process). The biasing is adaptive and is designed to approximate the free energy function associated with a reaction coordinate.

The main result is the consistency of the approach: almost surely, appropriate weighted occupation measures converge to the canonical distribution, in the large time limit.

This is joint work with Michel Benaïm (Neuchâtel).