Probing the limits of forward screening and inverse design of crystal materials

Inverse materials design is shifting materials discovery from forward prediction to targeted proposal of candidates that satisfy objectives under physical constraints. Here, we review recent advances in generative crystal structure modeling, multimodal learning, and closed-loop design pipelines for crystalline solids. We survey how modern generators learn chemical-structural priors from large databases to enable controllable sampling of periodic structures, and compare leading model classes including variational autoencoders, normalizing flows, autoregressive formulations, and diffusion models. Particular attention is given to how feasibility constraints and physical priors are enforced across the workflow, through representation choices, training objectives, sampling-time guidance, and post-generation screening and relaxation. We also discuss how multimodal learning fuses diverse materials modalities, including crystal structures, thermodynamic, electronic information, microscopy, spectroscopy, processing context, and scientific text, to construct a more universal, transferable representation of chemical space. In addition, diverse inverse-design strategies are examined, particularly those that integrate conditional generation with latent optimization, Bayesian optimization, reinforcement learning, and active learning. Finally, we highlight recurring failure modes, such as surrogate exploitation, diversity collapse, distribution shift, and the stability-synthesizability gap, and outline discovery-grade evaluation practices based on staged reporting of validity, novelty, uniqueness, stability, and cost.

De novo crystal generation seeks to discover materials that are not merely realistic, but also stable and novel. However, most existing generative models are trained to maximize the likelihood of observed crystals, which encourages samples to stay close to known materials yet not necessarily align with the criteria that matter in discovery. Our empirical analysis shows that current crystal generative models exhibit a clear conflict between stability and novelty: samples near the observed distribution tend to retain stability but offer limited novelty, whereas samples farther from it often lose stability rapidly. This suggests that the useful region for discovering crystals that are both stable and novel is extremely narrow. To move beyond this limitation, we introduce Crys-JEPA, a joint embedding predictive architecture for crystals that learns an energy-aware latent space preserving formation-energy differences. In this space, stability assessment can be reformulated as an embedding-based comparison against accessible training crystals, reducing the reliance on expensive energy evaluation and task-specific external references. Building on Crys-JEPA, we further develop a screening-and-refinement pipeline that identifies promising generated crystals and reintroduces them to refine the generative model. On MP-20 and Alex-MP-20 datasets, we achieve improvements over baselines up to 53.8% and 72.7% on V.S.U.N. metric, respectively.

Crystal structure prediction (CSP), which aims to predict the 3D atomic arrangement of a crystal from its composition, is central to materials discovery and mechanistic understanding. Crystal symmetry plays a crucial role in CSP, but given the composition in a unit cell, existing methods either struggle with the NP-hard combinatorial challenge of enforcing symmetry rigorously or rely on retrieving known templates, inherently limiting both physical fidelity and the discovery of genuinely new materials. To address this challenge, we introduce NextCrystal, a symmetry-driven generative framework that employs large language models to encode chemical semantics and directly generate fine-grained Wyckoff site patterns from atomic stoichiometry, eliminating reliance on database lookups. To overcome the combinatorial complexity of site assignments, we incorporate domain knowledge via an efficient, linear-complexity heuristic beam search, rigorously enforcing algebraic consistency between site multiplicities and atomic stoichiometry. By integrating this symmetry-consistent template into a diffusion backbone, the framework constrains the stochastic generative trajectory to a physically plausible geometric manifold. NextCrystal achieves state-of-the-art performance on stability, uniqueness, and novelty (SUN) benchmarks, as well as superior structural matching, establishing a rigorous paradigm for exploring previously unexplored crystallographic space without relying on prior structural templates. As a representative application, first-principles screening of HfO2 candidates generated by NextCrystal identifies a previously unreported dynamically stable Pnma phase, 0.056~eV/atom lower in energy than the conventional high-pressure Pnma phase.