Efficient Numerical Methods for Thermodynamic Averaging and Statistical Inference

Efficient Numerical Methods for Thermodynamic Averaging and Statistical Inference

-
Benedict Leimkuhler, University of Edinburgh
Fine Hall 214

Molecular models and data analytics problems give rise to gargantuan 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. One of the interesting ideas is to design stochastic schemes with close attention to the error in invariant measures. Another is to use negative feedback loop controls to regulate a noisy gradient or even the discretisation error itself.  To illustrate our approach, I will discuss several different examples including (i) efficient schemes for constrained stochastic dynamics improving accuracy and stability in bio-MD [1,2], and (ii) methods for Bayesian sampling f