Page 95 - Read Online

Li et al. J. Mater. Inf. 2025, 5, 43 https://dx.doi.org/10.20517/jmi.2025.17 Page 17 of 23

Applications in complex physical systems
Early applications of DHNNs have already demonstrated dramatic acceleration in electronic structure
calculations while achieving the accuracy of conventional DFT for key observables such as band-structure
predictions [Figure 4]. However, these proof-of-principle results represent only the first step. DHNNs are
now poised to move beyond benchmark systems and tackle a host of more demanding application-driven
challenges, for example non-adiabatic excited-state dynamics, complex magnetic phases, large-scale
quantum transport [Figure 4B]. Thus, it can push the frontiers of computational materials modeling into
new regimes of scale and physical complexity.

One significant frontier lies in the field of magnetic materials. Magnetic superstructures, including
phenomena such as altermagnets, magnetic skyrmions and spin-spiral magnets, are attracting immense
interest due to their emergent quantum physics. However, investigating these complex magnetic phases
traditionally with ab initio accuracy has been hampered by formidable computational costs. To surmount
this bottleneck, an extended DFT Hamiltonian framework, termed xDeepH, has been developed. This
framework integrates both atomic structures {R} and magnetic configurations {M}, while crucially adhering
to the equivariance requirements dictated by Euclidean and time-reversal symmetries. This sophisticated
architectural design is crucial in capturing the subtle magnetic effects that govern the spin dynamics of these
materials, demonstrating a pioneering approach to magnetic materials research.

Beyond ground-state properties, DHNNs are making significant strides in simulating excited-state
dynamics in solids. Non-adiabatic MD (NAMD) simulations are essential for understanding a wide range of
excited-state phenomena, including the energy transfer processes in solar cells and ultrafast carrier
dynamics in semiconductors. However, conventional DFT-based NAMD simulations are computationally
demanding and often suffer from accuracy limitations associated with standard exchange-correlation
functionals. Zhang et al. introduced N AMD, a framework that leverages E(3)-equivariant deep neural
2
[98]
Hamiltonians to address these challenges . Validated on prototypical semiconductors of TiO and GaAs,
2
N AMD accurately simulates electron-hole recombination behavior at a hybrid functional level (HSE06).
2
This framework hints at pathways to establish a more reliable and efficient paradigm for NAMD
simulations in complex condensed matter systems.

The ability of DHNNs to accelerate the density functional perturbation theory (DFPT) calculations
represents another pivotal advancement. Perturbation responses are fundamental to understanding a vast
spectrum of material properties, including temperature-dependent band gaps, non-radiative carrier
recombination, and electron-phonon driven phenomena such as thermal and electrical conductivity and
superconductivity. Deep learning frameworks, such as HamGNN and DeepH, are now being deployed to
streamline EPC calculations. These models achieve acceleration by training neural networks to predict key
quantities such as the Kohn-Sham potential or Hamiltonian matrix from DFT data of (perturbed) atomic
structures. The computationally expensive derivatives with respect to atomic displacements, crucial for
DFPT, are then efficiently obtained via automatic differentiation of the neural network or by
[79]
[85]
differentiating the network’s Hamiltonian predictions . This circumvents the need to solve the costly
Sternheimer equations for each perturbation mode, which is the bottleneck in traditional DFPT. These
models provide an efficient toolkit for investigating diverse EPC-related phenomena, enabling calculations
for large-scale systems with advanced functionals under perturbation, which were previously
computationally prohibitive. Furthermore, the success of DHNNs in DFPT for EPC calculations opens
exciting possibilities for generalizing these frameworks to investigate other types of perturbations, such as
strain and external fields.