Machine learning surrogate models for particle insertions and element substitutions

Aug 3, 2026

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Two machine learning-aided thermodynamic integration schemes are developed and compared to compute chemical potentials of atoms and molecules in condensed phases. One scheme uses particle insertion alone, while the other combines particle insertion with element substitution, each employing machine-learned potentials trained on first-principles datasets. Surrogate-model errors are corrected by thermodynamic integration from ML potentials to first-principles potentials, yielding first-principles chemical potentials accurately. The methods are applied to ions in water and produce identical real potentials within statistical error, matching experiments and simulations.

LanguageEnglish

CategoryResearch & Report

FormatPDF

Pages11

Reading Time28 min

AccessFree to download

Introduction

Chemical potential in condensed matter

Thermodynamic integration and particle insertion

Machine-learned force fields for acceleration

Correction from ML to first-principles potentials

Remaining challenges and coupling-path issues

arXiv :2409 . 19188v2 [physics .chem-ph] 4 Oct 2024 Sample title Machine learning surrogate models for particle insertions and element substitutions Ryosuke Jinnouchi1 Toyota Central R&D Labs., Inc., 41-1 Yokomichi, Nagakute, Aichi, 480-1192, Japan a) (Dated: 7 October 2024) Two machine learning-aided thermodynamic integration schemes to compute the chemical potentials of atoms and molecules have been developed and compared. One is the particle insertion method, and the other combines particle insertion with element substitution. In the former method, the species is gradually inserted into the liquid, and its chemical potential is computed. In the latter method, after the particle insertion, the inserted species is substituted with another species, and the chemical potential of this new species is computed. In both methods, the thermodynamic integrations are conducted using machine-learned potentials trained on first-principles datasets. The errors of the machine-learned surrogate models are further corrected by performing thermodynamic integrations from the machine-learned potentials to the first-principles potentials, accurately providing the first-principles chemical potentials. These two methods are applied to compute the real potentials of proton, alkali metal cations, and halide anions in water. The applications indicate that these two entirely different thermodynamic pathways yield identical real potentials within statistical error bars, demonstrating that both methods provide reproducible real potentials. The computed real potentials and solvation structures are also in good agreement with past experiments and simulations. These results indicate that machine learning surrogate models enabling the atomic insertion and element substitution provide a precise method for determining the chemical potentials of atoms and molecules. 1. INTRODUCTION The chemical potential of atoms and molecules in condensed matter is a crucial property that determines many physical characteristics, including the coexistence points of different phases, concentrations of minority species, solubility insolvents, free energy changes of chemical reactions, and redox potentials of electrochemical reactions. One of the ultimate goals of molecular dynamics (MD) simulations is to predict this property. However, accurate prediction using first principles (FP) methods is a highly challenging task. The difficulty can be well understood by considering the calculation of the actual potential of one or more atoms in a liquid. The real potential is defined as the change in free energy when the solute is transferred from a vacuum just outside the liquid surface into the liquid. The simplest approach to compute this free energy change is to perform thermodynamic integration (TI) 1,2 using the particle insertion method, where the interactions between the solute and the liquid are gradually switched on.3–5 While this brute-force method is simple, it suffers from poor statistical accuracy. Particularly in the initial stages, where an infinitesimally small interaction between the inserted solute and the liquid must be used, the integrand in TI can diverge to infinity because the not-yet-interacting atom can come very close to a solvent atom, experiencing a huge repulsive potential. Although this issue can be partially circumvented through variable transformations,5 most FP codes become unstable when two atoms are very close. Moreover, beyond the initial steps, a dramatic change in the solvation structure along the coupling constant requires extensive sampling, posing a significant challenge for FP calculations. Recently, machine learning force fields (MLFFs) have a)Electronic mail: [jryosuke@mosk.tytlabs.co.jp](jryosuke@mosk.tytlabs.co.jp) emerged as a powerful method that significantly accelerates the computation of free energy changes.6–11 When trained with a sufficient number of training datasets, MLFFs can accurately reproduce the potential

FAQs

What is the core objective of the two proposed ML-aided thermodynamic integration schemes?

To compute chemical potentials of atoms and molecules using thermodynamic integration accelerated by machine-learned surrogate potentials, while still delivering accurate first-principles results through error correction.

How do the particle insertion method and the particle insertion-plus-element-substitution method differ?

The particle insertion method gradually inserts the species and computes its chemical potential. The second method inserts a species first, then substitutes it with another species before computing the chemical potential of the new one.

How are errors from the machine-learned surrogate models addressed?

Errors are corrected by performing thermodynamic integration from the machine-learned potentials to first-principles potentials, which yields first-principles chemical potentials accurately.

What do the applications to ions in water show about reproducibility and accuracy?

Both thermodynamic pathways produce identical real potentials within statistical error bars, and the computed potentials and solvation structures agree well with past experiments and simulations.

Aug 3, 2026

Upload by Aurelia