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Li et al. J. Mater. Inf. 2025, 5, 43 Journal of
DOI: 10.20517/jmi.2025.17
Materials Informatics

Review Open Access

A critical review of machine learning interatomic
potentials and Hamiltonian

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Yifan Li , Xiuying Zhang , Mingkang Liu, Lei Shen *
Department of Mechanical Engineering, National University of Singapore, Singapore 117575, Singapore.
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Authors contributed equally.
* Correspondence to: Dr. Lei Shen, Department of Mechanical Engineering, National University of Singapore, 9 Engineering Drive
1, Singapore 117575, Singapore. E-mail: shenlei@nus.edu.sg
How to cite this article: Li, Y.; Zhang, X.; Liu, M.; Shen, L. A critical review of machine learning interatomic potentials and
Hamiltonian. J. Mater. Inf. 2025, 5, 43. https://dx.doi.org/10.20517/jmi.2025.17

Received: 22 Mar 2025 First Decision: 7 May 2025 Revised: 13 Jun 2025 Accepted: 20 Jun 2025 Published: 17 Jul 2025
Academic Editor: Xiang-Dong Ding Copy Editor: Pei-Yun Wang Production Editor: Pei-Yun Wang

Abstract
Machine learning interatomic potentials (ML-IAPs) and machine learning Hamiltonian (ML-Ham) have
revolutionized atomistic and electronic structure simulations by offering near ab initio accuracy across extended
time and length scales. In this Review, we summarize recent progress in these two fields, with emphasis on
algorithmic and architectural innovations, geometric equivariance, data efficiency strategies, model-data co-design,
and interpretable AI techniques. In addition, we discuss key challenges, including data fidelity, model
generalizability, computational scalability, and explainability. Finally, we outline promising future directions, such as
active learning, multi-fidelity frameworks, scalable message-passing architectures, and methods for enhancing
interpretability, which is particularly crucial for the field of AI for Science (AI4S). The integration of these advances
is expected to accelerate materials discovery and provide deeper mechanistic insights into complex material and
physical systems.

Keywords: Machine learning interatomic potentials, machine learning Hamiltonian, ab initio molecular dynamics,
density functional theory, AI for science

INTRODUCTION
Density functional theory (DFT) and molecular dynamics (MD) underpin modern computational materials

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