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Page 18 of 23 Li et al. J. Mater. Inf. 2025, 5, 43 https://dx.doi.org/10.20517/jmi.2025.17

Meanwhile, the realm of quantum transport in nanoelectronics is being revolutionized by DHNNs.
Simulating electron transport in nanoscale devices, particularly using the non-equilibrium Green’s function
(NEGF) method, is computationally intensive, hindering the design and optimization of advanced nano-
[64]
[99]
electronic components . Zou et al. presented the DeePTB-NEGF , a novel deep learning framework that
resolves this efficiency challenge. By integrating the DeePTB Hamiltonian approach with the NEGF
method, DeePTB-NEGF achieves first-principles accuracy while circumventing the computationally
expensive SCF iterations inherent in traditional DFT-NEGF methods. Validated through comprehensive
simulations of break junctions and carbon nanotube field-effect transistors (CNT-FETs), DeePTB-NEGF
demonstrates excellent agreement with experimental results and offers a powerful, high-throughput
approach for simulating quantum transport across diverse nano-electronic devices.

Although significant progress has been made in above mentioned complex physics scenario, there are many
complex physical systems for DHNNs, such as non-collinear magnets, topological quantum materials, high-
order anharmonic phonon interactions, superconductivity, amorphous structures and more. In non-
collinear antiferromagnets, DHNNs could improve the precision of modeling spin interactions and
magnetic phase transitions by efficiently capturing the underlying energy landscapes . Similarly, in
[100]
topological materials, these networks are expected to reveal nuanced insights into the interplay between
topology and electron dynamics, thereby supporting the design of quantum devices and spintronic
[101]
applications . Moreover, when dealing with complex electron-phonon interaction on thermoelectric
properties , DHNNs have the potential to elucidate phonon behavior and energy dissipation mechanisms
[102]
at multiple scales, offering a robust alternative to traditional simulation methods. These frontier
applications represent the next wave of DHNN innovation, building upon the established successes in
electronic structure, magnetic materials, excited-state dynamics, and quantum transport.

CONCLUSION AND OUTLOOK
ML-IAPs for MD and machine-learning Hamiltonian for electronic structure calculations have shown
significant promise in advancing materials simulations, offering near ab initio accuracy while enabling
access to larger length and time scales. The development of SOTA deep learning models has enabled more
accurate and efficient predictions of interatomic and electronic properties. These advancements are crucial
for the study and design of new materials, addressing the limitations of traditional methods such as MD and
DFT.

Despite the progress, several challenges remain. The accuracy of ML-IAPs is heavily dependent on the
quality and quantity of training data, which necessitates comprehensive data-sharing initiatives and
improved DFT calculations. Additionally, the computational demands of these models, especially for large-
scale simulations, are significant. Incorporating physical constraints and leveraging active learning can
enhance the performance of these models, but a balance between computational expense and accuracy must
be struck. The future of ML-IAPs is promising, with several key areas for development. Enhancing the
generality and accuracy of models through larger and more diverse training datasets is essential. The
integration of physical constraints and the adoption of coarse-graining techniques can further improve the
efficiency and applicability of these models. High parallel efficiency is another potential direction of ML in
materials science.

DHNNs are promising tools for electronic structure prediction but face challenges in generalizing across
diverse material systems and scaling to larger systems. Extending their applicability to encompass the entire
periodic table remains an ongoing research endeavor. Beyond electronic structures, DHNNs hold potential
in modeling complex physical systems such as non-collinear magnets, topological quantum materials, high-