Interpretable Machine Learning
Machine learning models can predict materials properties such as adsorption energies or electronic descriptors much faster than first-principles calculations, but flexible models like deep neural networks tend to learn correlations rather than causes, so they offer little physical insight on their own. Interpretable approaches try to recover that insight, either by building physical models into the network architecture so that intermediate quantities have physical meaning, or by attributing predictions to inputs after training (for example with Shapley values). See also d-band model.
Theory-infused neural networks for the d-band center (2024)
Huang, Wang, Kamanuru, Achenie, Kitchin and Xin embedded a rectangular d-band model, with a tight-binding second moment built from d-orbital radii and interatomic distances, inside a graph convolutional network (the TinNet framework). The network predicts physically meaningful corrections (a band-shape factor, a charge transfer coefficient, bond-length and orbital-radius scalings) that the physics module turns into the d-band center. On 12,165 fcc surface sites it reaches a mean absolute error of 0.032 eV, comparable to a black-box graph network, and SHAP analysis of the learned variables separates charge transfer (about 0.01 eV), strain and ligand effects (about 0.15 eV each) and a band-shape resonance effect (about 0.20 eV) (Huang et al. 2024). Summary: huang2024.
Opening the black box through mathematical structure (2025)
In a Comment on the future of modeling in chemical engineering, Kitchin, Alves and Laird argue that ML frameworks make it easy to use models as black boxes, and that more is possible when the mathematical structure of a model is understood (Kitchin et al. 2025). A regression neural network maps its inputs into a latent space in which the output is linear; for one hidden layer this amounts to an expansion in a basis of activation functions, so the choice of activation sets the properties of the trained model. Smooth activations such as hyperbolic tangent give non-convex models that are hard to optimize globally, whereas ReLU networks are piecewise linear and can be globally optimized with provable guarantees using tools such as OMLT. They also flag uncertainty quantification for ML models as unresolved, since Hessian-based methods are infeasible for networks with millions of parameters and Hessians of small models are often singular. Summary: kitchin2025; see also Differentiable programming.
Prediction versus insight in catalyst descriptors (2018)
Kitchin’s 2018 Comment on ML in catalysis contrasts an ML model that predicts the d-band center from up to nine elemental descriptors (moderately accurate with six) with an earlier physics-based model built only from site geometry and fitted d-orbital sizes, noting that the ML model predicts well but does not explain why its inputs matter (Kitchin 2018). He stresses that useful features require domain knowledge, and cites CO adsorption screening on core–shell alloys with physically motivated descriptors, where the model also revealed d-band shape and sp-band filling contributions missing from the simple d-band model. Summary: kitchin2018.
Physical versus symmetry features for chiral surface kinetics (2024)
Abdelmaqsoud and coworkers compared two linear ridge models for the enantiospecificity of tartaric acid decomposition on chiral Cu surfaces. A model on five chiral cubic harmonics, built only from the symmetry of the fcc lattice, fit the 507 measured orientations slightly better (test MAE 133 s) than one on 58 generalized coordination number features (138 s) and gave smoother predictions. The coordination-based model, however, could be interpreted: its weights pointed to a specific kink motif whose fraction on the surface correlates with enantiospecificity, explaining why Cu(11,3,1) is predicted to be optimal. The two models agreed on where the maximum lies to within 1.8 degrees, which the authors use as cross-validation of the extrapolation before experimental testing (Abdelmaqsoud et al. 2024). Summary: abdelmaqsoud2024.
Piecewise linear tree surrogates (2025)
Sunshine et al. argue that small decision trees with linear leaves keep the simplicity and explainability of a tree while capturing nonlinear multivariate behavior, and that the top-level splits often have physical meaning (Sunshine et al. 2025). Their hyperplane trees make this concrete for water thermodynamics: oblique splits line up with the boundary of the vapor-liquid envelope in the pressure-enthalpy plane, and each leaf is an explicit linear temperature model. Because the model is piecewise linear, it can be embedded exactly in a mixed-integer formulation, which connects to the argument for piecewise linear structure and global optimization in kitchin2025. Summary: sunshine2025.