Introducing physics-informed generative models for targeting structural novelty in the exploration of chemical space

Discovering materials with new structural chemistry is key to achieving transformative functionality. Generative artificial intelligence offers a scalable route to propose candidate crystal structures. We introduce a reliable low-cost proxy for structural novelty as a conditioning property to steer generation towards novel yet physically plausible structures. We then develop a physics-informed diffusion model that embeds this descriptor of local environment diversity together with compactness as a stability metric to balance physical plausibility with structural novelty. Conditioning on these metrics improves generative performance across diffusion models, shifting generation away from structural motifs that dominate the training data. A chemically grounded validation protocol isolates those candidates that combine plausibility with structural novelty for physics-based calculation of energetic stability. Both the stability and the novelty of candidates emerging from this workflow can however change when the full potential energy surface at a candidate composition is evaluated with crystal structure prediction (CSP). This suggests a practical generative-CSP synergy for discovery-oriented exploration, where AI targets physically viable yet structurally distinct regions of chemical space for detailed physics-based assessment of novelty and stability.

💡 Research Summary

The paper presents a novel framework for generating crystal structures that are both physically plausible and structurally novel, addressing a key limitation of current generative AI models which tend to reproduce the statistical patterns of their training data. The authors introduce two inexpensive, physics‑informed proxies: (i) Local‑Environment Diversity (MLED) and (ii) Compactness (C). MLED quantifies the variety of local atomic environments by assigning each atomic site to a reference coordination polyhedron, encoding both geometric and chemical information, smoothing the categorical descriptors with Gaussian kernels, and computing Shannon entropy over the resulting probability distributions. This yields a scalar that rises with both geometric motif diversity and chemical heterogeneity. Compactness is defined as the ratio of the summed nominal atomic volumes (based on tabulated atomic radii) to the unit‑cell volume, providing a lightweight estimate of how tightly atoms pack within a cell and correlating strongly with formation energy and stability.

These descriptors are embedded directly into a denoising diffusion generative model called PIGEN, which builds on the DiffCSP architecture. The model treats atom types as categorical variables and fractional coordinates plus lattice vectors as continuous variables diffused with periodic‑aware Gaussian noise. During training, a compound loss combines the standard diffusion objective with a compactness‑penalty term, forcing the reverse diffusion trajectory to stay on a physically reasonable manifold. Stochastic label dropout is employed so that the network learns both conditional and unconditional denoising pathways, enabling classifier‑free guidance (CFG) at sampling time. By specifying target values for C, MLED, or other properties (e.g., energy above hull, crystallographic complexity), the model can be steered toward desired regions of chemical space.

The authors train PIGEN on 607,684 stable inorganic crystals (up to 20 atoms) drawn from the Materials Project and Alexandria databases, preserving the full elemental diversity present in the data. During generation, the atom count is allowed to increase to 30, permitting extrapolation beyond the training size. Property‑conditioned variants (e.g., PIGEN|C=0.7, PIGEN|MLED=9) are evaluated. Results show that compactness values around 0.7 correspond to low formation energies, confirming C as a proxy for stability. Conditioning on MLED dramatically shifts the distribution of generated structures into the low‑probability tail of the training set: 43 % of PIGEN|MLED samples lie above the 99th percentile of the training MLED distribution, compared with 24 % for the energy‑above‑hull conditioned model. Moreover, the proportion of generated structures that do not match any of the 100 most frequent ICSD prototypes rises from 42 % (energy‑conditioned) to 67 % (combined MLED + C conditioning), demonstrating effective exploration of under‑represented coordination motifs.

A downstream validation pipeline filters candidates using the statistical potential (SPP) score, compositional novelty checks, and a 50 meV/atom energy‑above‑hull threshold. The filtered set is then subjected to crystal‑structure prediction (CSP), which explores the full potential‑energy surface at each composition. The authors observe that some candidates deemed stable by the proxy metrics become unstable after CSP, and vice versa, highlighting the complementary nature of AI‑driven generation and physics‑based optimization. This synergy enables rapid front‑end screening of vast regions of chemical space, followed by rigorous CSP assessment of the most promising, structurally distinct compositions.

In summary, the work introduces a physics‑informed diffusion model that integrates compactness and local‑environment diversity as conditioning signals, achieving a balance between plausibility and novelty. The approach outperforms baseline diffusion models in generating out‑of‑distribution structures, reduces reliance on dominant prototype families, and provides a scalable workflow that couples generative AI with CSP for accelerated discovery of new inorganic materials.