FastCSP: Accelerated Molecular Crystal Structure Prediction with Universal Model for Atoms

Crystal structure prediction (CSP) is fundamental to computational materials discovery. Generative models including CDVAE, DiffCSP, FlowMM, and CrystalFlow learn stable-crystal distributions directly, but diffusion and flow-matching inference requires tens to thousands of sequential network evaluations per candidate. We introduce uFlowCSP, a MeanFlow-based CSP model that learns the average, rather than instantaneous, probability-flow velocity. It generates a complete structure in one to five evaluations, delivering 5x-58x faster inference with equal or better performance. A chemistry- and symmetry-aware Transformer uses canonical atom ordering, global composition, and per-token chemistry embeddings. A coarse crystal-system token is used only during training; it provides additive gains, particularly improving space-group agreement despite being absent at inference, which remains formula-only. On MP-20 with 20 candidates per target, one step matches CrystalFlow (78.38% vs. 78.34%) with 100x fewer evaluations and about 10x lower wall-clock time. Five steps reach 83.64%, exceeding CrystalFlow (78.34% at 2,000 evaluations) and DiffCSP (77.93% at about 20,000), while using 20x fewer evaluations. uFlowCSP generates 10,000 structures in 0.39-1.31 minutes, versus 6.5 for CrystalFlow and 76.1 for DiffCSP. Under CSPBench's energy-ranked top-five structure-and-space-group criterion, five-step uFlowCSP reaches 72%/72%/65% structure, space-group, and consensus match rates. CrystalFlow reaches 78%/73%/68% at 100 steps but falls to 49%/32%/31% at five. Thus, uFlowCSP improves accuracy per network evaluation, not merely peak accuracy.

Organic crystal structure prediction (CSP) is a requirement for computational modelling of organic solids, but traditionally costs several CPU-years per molecule. Generative models such as OXtal dramatically reduce this cost by sampling stable organic crystal structures directly. However, OXtal forgoes explicit lattice parametrization in favour of modelling large crops of the bulk material with expensive triangle layers, which can incur a computational cost of minutes per molecule. In this paper, we reduce this to seconds with Clari, a large-scale flow matching model that generates redundancy-free unit cells and replaces triangle layers with pure pair-bias attention. Clari requires only atom types and bonds as input and does not need an RDKit-sanitizable input molecule, which expands its applicability to challenging chemistries such as fullerenes, metal complexes, and atom clusters. We further ablate key design choices such as auxiliary losses, timestep distributions, noise priors, and self-conditioning. On OXtal's test sets, we surpass OXtal's solve rate while obtaining a speedup of $15$-$30\times$. Because Clari also models explicit hydrogens, it supports inference-time scaling via direct energy ranking, without any decoration or relaxation step. When generating 150 crystals and selecting the top-30 by energy, we further improve solve rate while maintaining a speedup of $5$-$8\times$. We also introduce the CSD Teaching Subset as a new test split of diverse and complex molecules for future benchmarking. Our contributions enable CSP within seconds, making large-scale virtual screening of organic solids practical. Code is available at https://github.com/aspuru-guzik-group/clari.

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.