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<p>Ensemble machine learning (ML) methods have become pivotal in advancing materials science and physics, especially between 2023–2025, where predictive accuracy, uncertainty quantification, and model robustness are paramount. This review presents a comprehensive survey of modern ensemble approaches, focusing on bagging, boosting, stacking, and mixture-of-experts (MoE), and their applications across materials discovery, property prediction, and physical simulations. For instance, ensemble graph neural networks (GNNs) improved formation energy prediction with a mean absolute error (MAE) reduction from 0.072&#xa0;eV/atom (single CGCNN) to 0.054&#xa0;eV/atom (ensemble CGCNN), while stacked PINNs (Physics-Informed Neural Networks) reduced L<InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(^2\)</EquationSource> <EquationSource Format="MATHML"><math> <mmultiscripts> <mrow /> <mrow /> <mn>2</mn> </mmultiscripts> </math></EquationSource> </InlineEquation> errors by over 40% in inverse heat conduction tasks. Highlight trends such as: (i) ensemble GNNs combining CGCNN, GAT, and GraphSAGE for robust multi-property regression, (ii) PINN ensembles leveraging subdomain decomposition and model averaging for solving partial differential equations (PDEs), and (iii) hybrid frameworks integrating language models with structural GNNs for multi-modal property inference. Metrics like expected calibration error (ECE&#xa0;&lt;5%), negative log-likelihood (NLL), and prediction interval coverage are emphasized for uncertainty assessment. Benchmark datasets including Matbench, QM9, and OC20 demonstrate how ensembles outperform single learners across diverse domains. This review presents a roadmap for integrating ensemble methods with physics priors, aiding in the development of interpretable, transferable, and accurate scientific models.</p>

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Ensembles of Graph and Physics-Informed Machine Learning for Scientific Modeling in Materials Science: A Review

  • 期刊论文

  • 发表日期：

    2025年8月14日

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  • Dennis Delali Kwesi Wayo

摘要

Ensemble machine learning (ML) methods have become pivotal in advancing materials science and physics, especially between 2023–2025, where predictive accuracy, uncertainty quantification, and model robustness are paramount. This review presents a comprehensive survey of modern ensemble approaches, focusing on bagging, boosting, stacking, and mixture-of-experts (MoE), and their applications across materials discovery, property prediction, and physical simulations. For instance, ensemble graph neural networks (GNNs) improved formation energy prediction with a mean absolute error (MAE) reduction from 0.072 eV/atom (single CGCNN) to 0.054 eV/atom (ensemble CGCNN), while stacked PINNs (Physics-Informed Neural Networks) reduced L \(^2\) 2 errors by over 40% in inverse heat conduction tasks. Highlight trends such as: (i) ensemble GNNs combining CGCNN, GAT, and GraphSAGE for robust multi-property regression, (ii) PINN ensembles leveraging subdomain decomposition and model averaging for solving partial differential equations (PDEs), and (iii) hybrid frameworks integrating language models with structural GNNs for multi-modal property inference. Metrics like expected calibration error (ECE <5%), negative log-likelihood (NLL), and prediction interval coverage are emphasized for uncertainty assessment. Benchmark datasets including Matbench, QM9, and OC20 demonstrate how ensembles outperform single learners across diverse domains. This review presents a roadmap for integrating ensemble methods with physics priors, aiding in the development of interpretable, transferable, and accurate scientific models.