A critical review of machine learning interatomic potentials and Hamiltonian

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.