Neural surrogates for crystal growth dynamics with variable supersaturation: explicit vs. implicit conditioning

The spatiotemporal evolution of many physical, chemical, and biological systems is described by nonlinear partial differential equations (PDEs). Recently, deep neural network-based surrogate models have emerged as efficient alternatives to computationally expensive numerical PDE solvers. In this work, we propose a physics-constrained deep neural network as a surrogate model to learn the microstructural evolution of a binary mixture, in which conservation of the order parameter is imposed directly on the network output as a hard constraint. We train the model to accurately predict the time-evolution of phase separation in binary mixtures governed by the Cahn-Hilliard equation. We show that predictions from our trained surrogate model remain stable and accurate over long-time rollouts for both critical and off-critical mixtures and preserve the mixture composition throughout evolution. In contrast, a variant in which conservation is enforced only via a penalty term in the loss function drifts away from the initial composition and significantly loses predictive accuracy over the same rollout. This establishes that the hard constraint is essential for long-time stability and order parameter conservation. We also show that our model accurately captures the growth of domain size and is consistent with the Lifshitz-Slyozov domain-growth law. These results demonstrate the effectiveness of the proposed framework for modeling systems with conserved kinetics, and the construction extends directly to other systems with conserved quantities.

Grain growth is governed by the reduction in grain boundary energy and exhibits well-established statistical scaling laws. Developing data-driven surrogates that preserve these physical invariants while remaining computationally scalable remains challenging, especially in 3D. We present 3D-PRIMME (Physics-Regulated Interpretable Machine Learning for Microstructure Evolution) for learning three-dimensional grain growth dynamics. The model is trained using only two consecutive time steps yet accurately reproduces the linear coarsening law and preserves topological statistics over extended time scales. Despite being trained on a $100^3$ grid points with 512 grains, the learned evolution operator is applied to domains up to $1024^3$ grid points with 550000 grains without retraining, maintaining consistent kinetics and grain topology across orders-of-magnitude increases in system size. These results demonstrate that 3D-PRIMME learns a scale-independent and temporally stable local evolution rule, enabling efficient and robust large-scale surrogate prediction of 3D microstructure evolution.

A key question in benchmarking generative crystal reconstruction models is how the amount and type of crystallographic information provided to a generative model affects its ability to reconstruct atomic structures. Yet such comparisons often overlook the fact that models receive unequal information about the target during reconstruction, thereby confounding architectural conclusions. We present AtomBench, an extensible, model-agnostic framework for comparing generative models on a well-defined crystal reconstruction task (rather than \textit{de novo} generation), which we here apply to conventional superconductors. We train and evaluate four models, AtomGPT, CDVAE, FlowMM, and MatterGen, on the JARVIS Supercon-3D and Alexandria DS-A/B datasets, grouping them by the information each accesses at inference. Reconstruction fidelity is measured by the Kullback-Leibler divergence (KLD) and mean absolute error (MAE) of lattice parameters and the root-mean-squared displacement (RMSD) of atomic coordinates. We further introduce the continuous corrected RMSD (ccRMSD), a continuous measure of local geometric fidelity defined for every structure in the test set. MatterGen achieves the best atomic-coordinate reconstruction, followed by AtomGPT, while CDVAE reconstructs lattices most accurately, and FlowMM is the least accurate but fastest overall. We find that conditioning on critical temperature T$_c$ does not consistently improve fidelity. We also release AtomBench as an open-source Python package that reproduces all reported reconstruction metrics, figures, and tables from one or more benchmark files and supports direct submission to the JARVIS-Leaderboard. Any inverse model emitting crystal reconstructions can be benchmarked with \texttt{atombench}, and we encourage community use. https://github.com/atomgptlab/atombench