Improving Disordered Crystal Modeling with Nonlinear Atomic Embedding for Superconducting Materials

Accurately predicting properties like the superconducting critical temperature (T$_c$) is crucial for materials discovery, yet it remains challenging for materials exhibiting crystal disorder. Conventional deep learning models often represent substitutionally disordered sites using a simplified linear, occupancy-weighted average of atomic features. However, such linear mixing inadequately represents the complex, non-linear physics of disordered systems, where, as shown by perturbation theory and DFT, higher-order atomic interactions significantly impact material properties. We introduce the Non-Linear Disorder Network (NoLiDNet), designed to overcome this limitation. NoLiDNet module enhances the traditional linear sum by adding a non-linear component, learned via a residual Multi-Layer Perceptron (MLP), which acts on the embeddings of all co-located atomic species at disordered sites. This allows the model to capture complex higher-order interactions. Evaluations on the SuperCon3D and 3DSC$_{MP}$ datasets demonstrate that NoLiDNet significantly improves T$_c$ prediction accuracy, reducing Mean Absolute Error (MAE) compared to baseline models, particularly for materials with significant disorder. This work underscores the importance of capturing non-linear, multi-body atomic interactions for accurately predicting the T$_c$ of complex, disordered materials.