Machine Learning Force Field for Optimization of Isolated and Supported Transition Metal Particles

Aug 4, 2026

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Computational modeling is central to catalysis research, driving demand for methods that improve simulation accuracy while lowering computational cost. The study presents an energy-free machine-learning calculator combining three independently trained neural networks to predict both energies and atomic forces of metallic particles. A graph neural network estimates atomic energies for Pd nanoparticles, AuPd nanoalloys, and supported Pd crystallites with mean absolute error within 0.004 eV versus DFT, while forces are split into direction and norm networks achieving 0.080 eV/Å, with GNN interpretability tied to cohesion energy.

LanguageEnglish

CategoryResearch & Report

FormatPDF

Pages12

Reading Time30 min

AccessFree to download

Introduction

Energy-free machine-learning calculator

Neural network architecture and force decomposition

Results for Pd, AuPd, and supported Pd

Interpretability and physical grounding

This article is licensed under CC-BY 4.0 [pubs.acs.org/JCTC](pubs.acs.org/JCTC) Article Machine Learning Force Field for Optimization of Isolated and Supported Transition Metal Particles Alexandre Boucher, Cameron Beevers, Bertrand Gauthier, and Alberto Roldan * Cite This: [https://doi.org/10.1021/acs.jctc.4c01606](https://doi.org/10.1021/acs.jctc.4c01606) Read Online | | | | | | | | --- | --- | --- | --- | --- | --- | | ACCESS | Metrics & More | | Article Recommendations | | *sı Supporting Information | ABSTRACT: Computational modeling is an integral part of catalysis research. With it, new methodologies are being developed and implemented to improve the accuracy of simulations while reducing the computational cost. In particular, specific machine-learning techniques have been applied to build interatomic potential from ab initio results. Here, we report an energy-free machine-learning calculator that combines three individually trained neural networks to predict the energy and atomic forces of metallic particles. The investigated structures were a monometallic Pd nanoparticle, a bimetallic AuPd nanoalloy, and supported Pd metal crystallites on silica. Atomic energies were predicted via a graph neural network, leading to a mean absolute error (MAE) within 0.004 eV from density functional theory (DFT) calculations. The task of predicting atomic forces was split over two feed-forward networks, one predicting the force norm and another its direction. The force prediction resulted in a MAE within 0.080 eV/Å against DFT results. The interpretability of the graph neural network predictions was demonstrated by underlying the physics of the monometallic particle in the form of cohesion energy. 1. INTRODUCTION Many phenomena, such as the arrangement of metal atoms in gas-phase or supported metal particles, their interactions with a surface, or with substrates in a reactive environment, are governed by complex atomic interactions. The development of metal-based materials is instrumental to many industry sectors, [e.g. energy](e.g. energy 1)[ 1](e.g. energy 1)−3 and environmental control.4 Since its development in the 1960s,5 the density functional theory (DFT) has material as is the case of metal nanocoating or supported metal particles with a large ration of undercoordinated atoms.25−27 The recent progress in predicting potential energy surfaces (PES) based on representative data sets of spanned chemical space interpreted through machine learning (ML) architecturesled to neural network interatomic potentials (NNIPs) with nearDFT accuracy.28−35 ML has proven to be a powerful tool for accelerating computational research.28,29,34,36−41 NNIPs allow Downloaded via 86.10.2 14.249 on March 7, 2025 at 09:35:00 (UTC) . See [https://pubs.acs.org/sharingguidelines](https://pubs.acs.org/sharingguidelines) for options on how to legitimately share published articles. become the workhorse of condensed matter theoretical research and an instrumental tool to enhance and guide the development of metal-based technologies. Developing these materials, e.g. metal-based catalysts or highperformance alloys,6−13 requires exploring chemical systems that are too complex to be treated by DFT. Instead, classical force fields, e.g. Sutton-Chen, Finnis-Sinclair, or Gupta potentials,14−16 have been developed with the aim of reducing the computational resources necessary to explore these chemical spaces. Although widely employed over the past decades,17−21 these force fields’ accuracy does not reach that of ab initio calculations, e.g. DFT.22−24 Furthermore, the parametrization and formulation of these force fields, based on the bulk properties of the material, make them fundamentally unable to describe accurately the energies and forces of small particles or systems involving an interface between the metal and another for highly efficient computation at a cost up to 1000 times cheaper than an accurate DFT calculation.

FAQs

What problem does the proposed machine-learning force field address?

It targets the trade-off between simulation accuracy and computational cost in catalysis modeling by learning interatomic potentials from ab initio results.

How are atomic energies predicted in this method?

Atomic energies are predicted using a graph neural network trained on ab initio data, achieving a mean absolute error within 0.004 eV compared with DFT.

How are atomic forces handled by the calculator?

Force prediction is split into two feed-forward networks: one predicts the force norm and the other predicts its direction, yielding a mean absolute error within 0.080 eV/Å against DFT.

Aug 4, 2026

Upload by Levi