CTMS Adventures In Theory Lectures Seminar
Monday, September 19, 2016, 4:30pm, 119 Physics
Ben Leimkuhler (University of Edinburgh)
From Molecular Dynamics to Large Scale Inference
Abstract:
Molecular models and data analytics problems both give rise to enormous systems of stochastic differential equations (SDEs) whose paths are designed to ergodically sample multimodal probability distributions. An important challenge for the numerical analyst (or the data scientist, for that matter) is the design of numerical procedures to generate these paths. One of the interesting ideas is to construct stochastic numerical methods with close attention to the error in the invariant measure (reducing bias in statistical computations) [1]. Another is to redesign the underlying stochastic dynamics to enhance sampling, for example by incorporating a local rescaling of variables. I will illustrate these ideas with various examples, including a geodesic integrator for constrained Langevin dynamics [2] and an ensemble sampling strategy for distributed Bayesian inference [3].

[1] B. Leimkuhler and C. Matthews, Rational construction of stochastic numerical methods for molecular sampling, Applied mathematics research express, 2013, doi: 10.1093/amrx/abs010
[2] B. Leimkuhler and C. Matthews, Efficient molecular dynamics using geodesic integration and solvent-solute splitting, Proceedings of the Royal Society A, 2016, doi: 10.1098/rspa.2016.0138
[3] B. Leimkuhler, C. Matthews and J. Weare, Ensemble preconditioning for Markov chain Monte Carlo simulation, Arxiv: https://arxiv.org/abs/1607.03954

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