Kernel-Based Machine Learning for Efficient Simulations of Molecular Liquids.

René Scheid,Tristan Bereau,Christoph Scherer,Denis Andrienko

doi:10.1021/acs.jctc.9b01256

Abstract

Current machine learning (ML) models aimed at learning force fields are plagued by their high computational cost at every integration time step. We describe a number of practical and computationally efficient strategies to parametrize traditional force fields for molecular liquids from ML: the particle decomposition ansatz to two- and three-body force fields, the use of kernel-based ML models that incorporate physical symmetries, the incorporation of switching functions close to the cutoff, and the use of covariant meshing to boost the training set size. Results are presented for model molecular liquids: pairwise Lennard-Jones, three-body Stillinger–Weber, and bottom-up coarse-graining of water. Here, covariant meshing proves to be an efficient strategy to learn canonically averaged instantaneous forces. We show that molecular dynamics simulations with tabulated two- and three-body ML potentials are computationally efficient and recover two- and three-body distribution functions. Many-body representations, decomposition, and kernel regression schemes are all implemented in the open-source software package VOTCA.

Highlights

Machine learning (ML) techniques have a long history of interpolating the high-dimensional potential energy surface (PES) of molecular systems.[1−4] Access to an accurate PES enables the simulation of the system’s dynamics
An early realization of this aspect was demonstrated by Behler and Parrinello, who relied on symmetry functions to incorporate translational and rotational invariance:[13] If the physics of the problem does not depend on arbitrary translations, encode particle geometries by means of relative distances
A number of molecular representations have since built on these ideas to offer more efficient learning performance.[11,14−16] Other aspects that aim at incorporating physics include local dynamical symmetries found in molecules[17] and the learning of tensorial properties.[18−20]

Summary

INTRODUCTION

Machine learning (ML) techniques have a long history of interpolating the high-dimensional potential energy surface (PES) of molecular systems.[1−4] Access to an accurate PES enables the simulation of the system’s dynamics. CG is an appealing resolution in soft matter due to its ability to reach longer length and time scales.[35,36] We focus on bottom-up strategies that systematically derive a CG model from higher-level microscopic information.[37] Consistency between the equilibrium probability densities of the two models leads to the many-body potential of mean force (MB-PMF), which effectively replaces the coveted PES.[38] One practical approach to building a CG model is force matching (FM) or multiscale coarse-graining (MS-CG),[38−40] which projects the MB-PMF into the space of force fields defined by the CG basis set Both kernel-based and neural-network approaches have recently been applied to solving the MS-CG problem.[30,41,42] Akin to the study of John and Csań yi,[30] we solve the MS-CG problem using kernels on both two- and three-body interactions, but we project the resulting decompositions onto computationally efficient tabulated potentials. We discuss both parametrization strategies and structural accuracy of the resulting condensed phase of liquid water

KERNEL-BASED REGRESSION FOR FORCE FIELDS

TWO-BODY LENNARD-JONES FLUID

CUTOFFS AND SWITCHING FUNCTIONS

COVARIANT MESHING

COARSE-GRAINING

11. CONCLUSIONS

■ ACKNOWLEDGMENTS

■ REFERENCES