Explainable Latent-Space and Anomaly-Sensitive Learning for Thermodynamic Crystal Stability Prediction

Thermodynamic stability prediction remains a fundamental challenge in computational materials science because of the enormous size and structural complexity of crystal design space. In this study, we designed and developed a multimodal and explainable artificial intelligence framework for latent-space characterization of crystalline material stability using graph neural networks, manifold learning, anomaly detection, and explainable artificial intelligence (XAI). A total of 10,000 crystalline materials from the Materials Project database were analyzed using crystallographic and physicochemical descriptors. Hybrid feature representations comprising up to 182 descriptors were constructed from MAGPIE compositional features, lattice parameters, average bond distances, and partial radial distribution function (pRDF) descriptors. Crystal structures were further encoded using Crystal Graph Convolutional Neural Networks (CGCNNs), generating 64 dimensional graph embeddings. Subsequently, five manifold learning techniques, namely UMAP, t SNE, Diffusion Maps, Autoencoder (AE), and Variational Autoencoder (VAE), were comparatively assessed across latent spaces with dimensionalities of 2, 4, 8, 16, and 32. The resulting latent representations were analyzed using six anomaly detection algorithms, yielding 150 experimental configurations. Among all evaluated models, UMAP combined with Deep SVDD in a 4-dimensional latent space achieved the best performance, with an AUROC of 0.684, Precision@K of 0.906, and F1-score of 0.252. Isolation Forest and VAE-ELBO anomaly scoring achieved AUROC values of 0.677 and 0.665, respectively. In contrast, highly compressed 2-dimensional latent spaces produced AUROC values concentrated around 0.494–0.505, indicating limited anomaly separability. XAI analyses using SHAP, LIME, and GNN edge-importance mapping showed that thermodynamic instability was strongly associated with localized manifold-boundary regions and structurally anomalous crystal environments. Overall, the proposed framework demonstrates the potential of manifold-aware explainable AI for interpretable crystal stability analysis and anomaly-sensitive materials discovery.