Efficient sampling using stochastic differential equations, from molecular dynamics to large scale inference
Benedict Leimkuhler, University of Edinburgh


Molecular models and data analytics problems give rise to large systems of stochastic differential equations (SDEs) whose paths ergodically sample multimodal probability distributions. An important challenge for the numerical analyst (or the chemist, or the physicist, or the engineer, or the data scientist) is the design of efficient numerical methods to generate these paths. For SDEs, the numerical perspective is just maturing, with important new methods (and, even more important, new procedures for their construction and analysis) becoming available. I will discuss examples of efficient schemes for stochastic sampling dynamics arising in our work. I will also touch on the interplay between numerical schemes arising in physical and statistical contexts.