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Page 6 of 15 Wu et al. J. Mater. Inf. 2025, 5, 15 https://dx.doi.org/10.20517/jmi.2024.67

PIML FOR ELECTROCATALYSTS
ML has achieved great success in catalysis research. However, the predictions made by ML models are based
on previous experiences rather than on understanding the underlying mechanism. While those ML models
demonstrate high accuracy in interpolation, they fall short in inspiring chemists to creatively discover
unseen electrocatalysts because they are not effective for extrapolation. One solution to this limitation is to
develop PIML for electrocatalyst design with better generalization and interpretability, in which the models
will naturally give physical or chemical explanations for their predictions. The other solution is the XAI
approach. Although both PIML and XAI models aim to enhance model interpretability, they differ
fundamentally in their approaches and implementation. PIML models incorporate physical and chemical
laws directly into the model architecture and training process, ensuring that predictions are consistent with
established scientific principles. In contrast, XAI methods mainly focus on post-training analysis and
interpretation of model behavior. Each approach has its own limitations: PIML models are restricted to
systems with well-defined physical laws and might struggle with complex or unknown physical systems,
while XAI methods may produce inconsistent or contradictory interpretations due to their high sensitivity
to hyperparameters. Importantly, PIML and XAI are complementary: PIML can leverage XAI techniques to
better illustrate how physical/chemical principles affect model outputs; XAI can increase its credibility with
[76]
the help of PIML . This section will briefly introduce these methods and their applications in the
electrochemical realm.

PIML models
PIML models are often implemented through adding physical constraints. This can be achieved by
modifying loss functions, adding more physics or chemistry-based features, and adapting model
architecture. Based on the architecture of the models, they can be grouped as GNN-based, kernel-based, or
equivariant GNN-based models.

GNN-based model
TinNet is one of the most famous GNN-based models that integrate the d-band theory into the model to
[77]
predict the adsorption energies of adsorbates on transition-metal surfaces . Two sequential parts are
included for the TinNet model, i.e., the regression module and the theory module. The regression module is
similar to the approach used in the crystal graph convolutional neural network (CGCNN), where the
flattened readout features of the adsorbate-substrate system can be integrated with the d-band theory to
make the final prediction of adsorption energies based on minimization of the loss function between the
predicted properties and physical features in the output layer . By considering the metal sp-state, d-state
[58]
(including Pauli repulsion and orbital hybridization), and the projected DOS onto the adsorbate orbitals,
the d-band theory for chemical bonding at the metal surface can be established [Figure 2A]. Compared to
the model with the fully connected neural network (FCNN) and CGCNN, TinNet shows comparable
prediction performance but with physical insights, highlighting the importance of the frontier molecular
orbital theory and electronic structure methods. Moreover, TinNet demonstrates improved generalization
capability because it is applicable to varied adsorbates and facets, as shown in Figure 2B-D.

Another attempt is to integrate local bonding information into ML framework design. Ghanekar et al.
proposed the adsorbate chemical environment-based graph convolution neural network (ACE-GCN) ,
[78]
which is a screening workflow considering diverse atomistic configurations [Figure 2E]. The performance of
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ACE-GCN was successfully verified by the cases of NO adsorption on a Pt Sn (111) alloy surface [Figure 2F]
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and OH adsorbed on a stepped Pt (221) facet [Figure 2G]. Both cases are very complicated in
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electrocatalysis: one involves strong binding of adsorbates on low-symmetry alloyed surfaces, while the
other pertains to directionally dependent adsorption on defective surface structures. The chemical insights