SWItched DIffusions : Metastability and Stochastic algorithms – SWIDIMS

The SWIDIMS project is concerned with the study and use in stochastic algorithms of switched diffusion processes, which describe the evolution in time of a system that evolves according to a collection of stochastic differential equations, switching from one to the other at random times. The seminal objective of the project is to use such processes in stochastic algorithms for exploring high-dimensional non-convex energy landscapes, which is the bottleneck in many problems of optimization or Markov Chain Monte-Carlo sampling. The design and study of such algorithms then necessitates a better understanding of this class of processes, and the development of general tools to control their long-time behaviour. A key motivation is that switching between flows with different stable domains should foster the transitions between such domains. A particular attention is thus paid to the so-called metastable regime, i.e. when the intensity of the noise vanishes and transitions are rare.