Self-learning path integral hybrid Monte Carlo with mixed ab initio and machine learning potentials for modeling nuclear quantum effects in water

TL;DR

This paper introduces a self-learning hybrid Monte Carlo method combining ab initio and machine learning potentials to efficiently model nuclear quantum effects in water, achieving near ab initio accuracy with significantly reduced computational cost.

Contribution

The paper presents the SL-PIHMC-MIX method, extending previous self-learning Monte Carlo techniques to path integral simulations with mixed potentials for larger systems.

Findings

Exact reproduction of ab initio PIMD structure with fewer evaluations

Significant reduction in computational cost for simulations

Extension of self-learning Monte Carlo to path integral methods

Abstract

The introduction of machine learned potentials (MLPs) has greatly expanded the space available for studying Nuclear Quantum Effects computationally with ab initio path integral (PI) accuracy, with the MLPs' promise of an accuracy comparable to that of ab initio at a fraction of the cost. One of the challenges in development of MLPs is the need for a large and diverse training set calculated by ab initio methods. This data set should ideally cover the entire phase space, while not searching this space using ab initio methods, as this would be counterproductive and generally intractable with respect to computational time.In this paper, we present the self-learning PI hybrid Monte Carlo Method using a mixed ab initio and ML potential (SL-PIHMC-MIX), where the mixed potential allows for the study of larger systems and the extension of the original SL-HMC method [Nagai et al., Phys. Rev. B 102, 041124 (2020)] to PI methods and larger systems. While the MLPs generated by this method can be directly applied to run long-time ML-PIMD simulations, we demonstrate that using PIHMC-MIX with the trained MLPs allows for an exact reproduction of the structure obtained from ab initio PIMD. Specifically, we find that the PIHMC-MIX simulations require only 5,000 evaluations of the 32-bead structure, compared to the 100,000 evaluations needed for the ab initio PIMD result.