Path Space Markov Chain Monte Carlo Methods for Molecular Simulation

Citation

Rosa-Raíces, Jorge Luis (2022) Path Space Markov Chain Monte Carlo Methods for Molecular Simulation. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/10jr-hg67. https://resolver.caltech.edu/CaltechTHESIS:03292022-234015177

Abstract

Path space Markov-chain Monte Carlo (McMC) provides a versatile framework for simulating the structure and dynamics of condensed-phase systems aptly described by classical and quantum Boltzmann statistics. This thesis comprises our efforts to design, analyze and improve path space McMC algorithms to achieve numerically advantageous, and physically accurate, simulation of molecular processes across a range of scales. To improve molecular dynamics (MD) simulations of atomically resolved systems exhibiting pronounced nuclear quantum effects, we introduce a family of integrators for non-preconditioned path-integral MD exhibiting dimension-free statistical accuracy and efficiency, and enabling a many-fold increase in time-step stability relative to conventional approaches at no additional computational cost or implementation complexity. The integrators come with robust performance guarantees that are borne out in thermostatted ring-polymer MD simulations of realistic condensed-phase models. Concurrently, toward extending the range of accessible timescales in stochastic MD simulations of mesoscale coarse-grained molecular systems, we introduce a parallel-in-time integrator for the overdamped Langevin equation based on McMC evaluation of a path-integral representation of the many time-step stochastic MD transition kernel. The parallel-in-time integrator achieves simultaneous integration of multiple stochastic MD time-steps at no greater wall-time cost and with no lesser accuracy than a standard Euler--Maruyama integrator does in serial, and thus instantiates new opportunities to accelerate stochastic dynamics simulations on massively parallel computer architectures. Our work along these two methodological avenues extends the utility of path space McMC across applications in molecular simulation and has broader implications in other disciplines that require accurate and efficient simulations of Markov diffusion processes in state spaces or path spaces.

Thesis Files