Abstract

 In this talk, we present some recent progresses in random bath molecular dynamics. We first discuss the sum-of-exponentials (SOE) and sum-of-Gaussians (SOG) approximations of kernel functions, and present a novel de la Vallée-Poussin and model reduction method for constructing kernel independent SOE and SOG. A random-batch SOG method is then present for long-range interactions in molecular dynamics, where the far part of the SOG series is solved in the Fourier space with the random-batch importance sampling. Finally, we introduce our recent work on symmetric preserving and energy stable time integration for molecular dynamics with stochastic forces. Numerical results are present to demonstrate the performance of the algorithms.