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

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The introduction of machine learned potentials (MLPs) has greatly expanded the space available for studying Nuclear Quantum Effects computationally with abinitio path integral (PI) accuracy, with the MLPs' promise of an accuracy comparable to that of abinitio 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 abinitio methods. This dataset should ideally cover the entire phase space, while not searching this space using abinitio 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 abinitio 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 abinitio PIMD. Specifically, we find that the PIHMC-MIX simulations require only 5000 evaluations of the 32-bead structure, compared to the 100 000 evaluations needed for the abinitio PIMD result.