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Li et al. J. Mater. Inf. 2025, 5, 43 https://dx.doi.org/10.20517/jmi.2025.17 Page 19 of 23

order anharmonic phonon interactions, and superconductivity. Enhancing the explainability of DHNNs is
crucial for advancing scientific understanding, which could involve integrating interpretability techniques
such as mapping learned Hamiltonians to graph representations. Future research should focus on
combining the predictive power of DHNNs with interpretable scientific models to accelerate scientific
discovery.

DECLARATIONS
Acknowledgments
The authors thank Dr. Ziduo Yang for his insightful discussions and valuable suggestions. We also thank
Ying Zhang for her generously sharing and meticulously collecting literature, particularly related to
machine-learned Hamiltonians. Additionally, we acknowledge computational resources and support
provided by National University of Singapore.

Authors’ contributions
Conceived and designed this review: Shen, L.
Conducted the machine learning interatomic potentials section: Li, Y.
Conducted the machine learning Hamiltonian part: Zhang, X.; Liu, M.; Li, Y.
Drafted manuscript: Li, Y.; Zhang, X.; Liu, M.
Edited the manuscript: Shen, L.
All authors reviewed the results and approved the final version of the manuscript.

Availability of data and materials
Not applicable.

Financial support and sponsorship
This work was supported by Singapore MOE Tier 1 (No. A-8001194-00-00) and Singapore MOE Tier 2 (No.
A-8001872-00-00).

Conflicts of interest
Shen, L. is an Editorial Board Member of Journal of Materials Informatics but is not involved in any steps of
editorial processing, notably including reviewer selection, manuscript handling, or decision-making, while
the other authors have declared that they have no conflicts of interest.

Ethical approval and consent to participate
Not applicable.

Consent for publication
Not applicable.

Copyright
© The Author(s) 2025.

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