Page 94 - Read Online

Page 16 of 23 Li et al. J. Mater. Inf. 2025, 5, 43 https://dx.doi.org/10.20517/jmi.2025.17

Deep Hamiltonian model for physical interpretation
DHNNs have rapidly established themselves as a transformative AI paradigm for materials discovery,
achieving near-DFT accuracy across a spectrum of phenomena from MD and electron-phonon coupling
(EPC) to quantum many-body interactions. By learning directly from high-fidelity training data and
embedding core physical laws into their architectures, DHNNs offer a unified, data-driven alternative to
conventional simulation workflows. Nevertheless, despite their outstanding predictive performance, these
models remain largely “black boxes” with limited transparency into the mechanistic features driving their
outputs. This opacity poses a significant barrier to scientific insight. Without interpretable representations
of the learned Hamiltonian landscape, it is challenging to extract the underlying physics or to validate
model predictions against established theoretical frameworks. Enhancing the interpretability of DHNNs is
therefore essential to harness their full potential as tools for both prediction and discovery.

In contrast to the black-box nature often associated with deep learning, including DHNNs, traditional
computational methods in physics, such as DFT, have long provided a framework for understanding
physical phenomena through interpretable quantities. Recent advancements in the explainable GNNs offer
a potential approach for the interpretability. GNN explainability methods, focusing on identifying the
importance of nodes and edges within graph-structured data, have shown promise in attributing model
[93]
predictions to specific structural features . For instance, the ability to assign scientific meaning to nodes
representing atoms and edges representing bonds in molecular graphs, as demonstrated in GNN explainer
frameworks LRI and SubMT, highlights the potential to connect model interpretations to real-world
scientific concepts [94,95] . Beyond GNNs, variational autoencoders (VAEs) offer a complementary path to
interpretability for deep learning in physics. Visualizing VAE latent spaces, for example, via t-SNE, reveals
physically meaningful representations learned in an unsupervised manner. Smooth trajectories and
clustering in latent space, reflecting physical properties such as wavefunction smoothness and material
[96]
similarity, demonstrate that VAEs can autonomously encode interpretable physical information . This
approach provides a crucial step towards bridging the interpretability gap in DHNNs, moving beyond
“black box” predictions to deeper physical understanding.

Therefore, a crucial next step in the development of DHNNs lies in enhancing their explainability, moving
beyond mere accuracy towards models that offer genuine scientific understanding, for example integrating
interpretability techniques with DHNNs . Exploring methods to map the learned Hamiltonian and its
[97]
associated energy landscape within a DHNN to a graph representation, where nodes and edges could
represent physical entities and interactions, could enable the application of GNN explainability tools. This
could potentially reveal which physical components or interactions within the Hamiltonian learned by the
DHNN are most salient for predicting specific physical phenomena. Furthermore, investigating the
gradients of the DHNN’s energy function with respect to input features, and visualizing these gradients on a
graph representation of the system, may unveil crucial physical insights driving the model’s predictions.
Future research should prioritize the development of methods that integrate the predictive power of
DHNNs with the interpretable scientific models. By fostering the creation of truly explainable DHNNs, we
can unlock their full potential to accelerate scientific discovery, providing not only accurate simulations but
also transparent and insightful tools for advancing our understanding of the physical world.