Crystal

Crystal generators can now propose periodic structures, but their control interfaces remain poorly matched to the mixed descriptors used in materials design. Text provides a compact way to combine composition, symmetry, prototype and property cues, yet it has not been clear whether such information can steer flow-based crystal generation. Here we introduce TFMat, a text-conditioned flow-matching framework that uses structured materials language as a semantic prior for a CrystalFlow generator. Across Perov-5, Carbon-24 and MP-20 crystal structure prediction benchmarks, TFMat improves one-candidate match rates over CrystalFlow and reaches a 92.04% MP-20 match rate with 20 candidates; in de novo generation, it improves element-count and density distribution alignment while retaining coarse property consistency in composition-selected outputs. These results position structured text as an inspectable control layer for translating human-readable materials intent into candidate crystals for downstream simulation and validation.

Learning materials properties from scarce labels and unlabeled crystals is a central challenge for data-driven materials discovery. We present SemiMat, a controlled benchmark for semi-supervised materials property regression, and MatRank, a reliability-weighted objective for continuous pseudo-label uncertainty. SemiMat fixes labeled and unlabeled crystal inputs, graph-backbone interfaces, validation-only checkpoint selection, held-out test reporting, normalized MAE (NMAE), and method-rank summaries across six scarce-label tasks, four graph backbones, and five predefined split runs. MatRank builds pseudo-targets from labeled anchors, weights them by local reliability and weak-prediction agreement, trains weak and strong graph views consistently, and adds ranking signals so that unlabeled crystals shape both values and candidate order. Across the retained 24 backbone-task blocks, one fixed MatRank objective gives the lowest aggregate held-out test NMAE (0.896) and best average method rank (2.208). The component, OOD, and generated-pool diagnostics identify where the gain is reliable and where further screening evaluation remains necessary. Code is available at https://github.com/littlepeachs/SemiMat.

Generating crystals has recently attracted significant interest due to their broad applications in materials science. However, existing generative models struggle to produce complete crystallographic specifications, limiting their ability to capture global symmetry and structural dependencies. In particular, current state-of-the-art approaches generate crystals only up to site symmetries and rely on sampling space groups from empirical distributions during generation. Inspired by \emph{spontaneous symmetry breaking} in physics, where crystals break symmetries under external conditions, we propose a novel diffusion-based framework that generates full structure specifications by reversing from the lowest-symmetry priors. Our method leverages a Markovian jump-diffusion process to model these symmetry-breaking dynamics, enabling it to traverse different space groups in a physically motivated manner. Our model, dubbed \emph{Symmetry-breaking Crystal Diffusion} (SbCD), introduces a principled approach to explicitly incorporate inter-space-group transitions into the generative process. In de novo generation experiments on MP20 and MPTS-52, SbCD outperforms its symmetry-preserving counterpart by a substantial margin, offering a promising perspective for generative modeling of crystalline materials.

The search for new crystalline materials spans an enormous compositional and structural space. Generating candidates in this space requires jointly modeling discrete crystallographic symmetry, elemental composition, and continuous geometry. We introduce DynaCrys, a generative model for crystals in which the space group co-evolves with Wyckoff occupations and elements through a coupled symbolic diffusion process. The structured space-group transitions follow crystallographic group-subgroup relations. As the space group changes, a shared, pretrained symmetry codebook provides both the legality-constrained stochastic decoder and the symmetry-constrained crystal-geometry model with a common representation of the corresponding Wyckoff vocabulary. Across large-scale evaluations using two independent relaxation-and-evaluation engines, DynaCrys achieves best-in-class performance in symmetry-aware discovery of stable, unique, and novel crystals, both overall and under the additional requirement of nontrivial post-relaxation symmetry. It also enables fast sampling while generating structures with consistently low relaxation-induced structural displacements.

Test-time scaling can correct difficult text-to-SQL queries, but the extra computation is normally discarded after each answer. Systems increasingly retain verified repair episodes, yet evaluations still report one end-to-end score. It cannot distinguish replay on recurring questions from help on unseen questions, or identify the responsible memory choice. We call measuring this future value the crystallization problem. Our controlled evaluation holds the single-shot solver fixed and varies one memory choice at a time. We separately measure replay, cross-question retention, and held-out same-database transfer. On BIRD, storing verified corrected queries improves held-out first-attempt accuracy by 4.34 percentage points. This gain captures 44.4% of the accuracy headroom provided by on-demand repair on the same questions. Controlled interventions identify database-specific content as the main operating ingredient. Reliable verification and broader retrieval coverage yield supported gains; richer formats and elaborate retrievers do not. Open-source code, evaluation artifacts, and reproduction instructions are available at https://github.com/ai-jiaqian/text-to-sql-memory-crystallization.

Flow-based generative models can efficiently produce candidate structures for crystal structure prediction (CSP), but their pretrained objectives do not directly optimize downstream target recovery. Reinforcement-learning post-training offers a flexible solution, yet existing approaches rely primarily on energy rewards and coordinate-only stochastic policies. Predicted energy does not identify the reference polymorph, while reward-driven concentration can reduce the candidate coverage required for Top-N recovery. We introduce CrystalGRPO, a CSP-aligned post-training framework that extends existing ODE-to-SDE policy constructions to the joint coordinate--lattice state. CrystalGRPO combines MACE-predicted energy with a StructureMatcher-based recovery score and provides two operating modes: CrystalGRPO-Q, which prioritizes single-draw recovery, and CrystalGRPO-C, which combines full-trajectory reference regularization with a coverage-aware group advantage to preserve finite-budget target recovery. Across MP-20 and MPTS-52 with PXRDGen and OMatG backbones, both variants reduce one- and twenty-sample RMSE relative to coordinate-only reinforcement in all four backbone--dataset settings. CrystalGRPO-Q consistently improves Top-1, whereas CrystalGRPO-C achieves a higher Top-20 across all settings.

Accurate prediction of crystal properties remains a key challenge in computational materials science. While graph neural networks (GNNs) such as CGCNN, MEGNet, ALIGNN, and SchNet have shown strong performance, they primarily represent crystals at the atomic level and implicitly learn local chemical environments through message passing. However, many material properties are governed by coordination polyhedra, the fundamental structural units formed by atoms and their neighboring atoms. To address this limitation, we propose the Coordination Polyhedron Graph Network (CPGN), a multi-scale GNN that jointly learns atomic, bond, and coordination-polyhedron representations. CPGN constructs three coupled graphs: an atom graph encoding elemental and bonding information, a line graph capturing angular interactions, and a coordination polyhedron graph describing Voronoi-derived local environments through corner-, edge-, and face-sharing relationships. Physically meaningful geometric descriptors are incorporated for each polyhedron, while an interleaved message-passing mechanism with bidirectional cross-attention enables effective information exchange across structural levels. Extensive evaluations on the Materials Project, JARVIS-DFT, and QM9 benchmark datasets demonstrate that CPGN outperforms existing state-of-the-art GNN models. It achieves a formation-energy MAE of 0.060 eV/atom and a band-gap MAE of 0.292 eV on the Materials Project, while providing competitive multi-property prediction on JARVIS-DFT and superior HOMO prediction on QM9. The results highlight that explicit modeling of coordination polyhedra improves crystal representation learning and enables accurate, physically interpretable prediction of material properties.

AI agents deployed for IT operations are typically permanent cost centers because every execution requires full LLM inference, even for previously solved problems. This paper introduces progressive crystallization, a lifecycle that treats agent exploration as a discovery mechanism rather than a permanent execution model. It defines a three-stage execution taxonomy, from fully agent-orchestrated to hybrid to fully deterministic workflows, together with an evidence-based promotion mechanism that converts repeatedly validated agent behaviors into cheaper and more reproducible deterministic workflows, while automatically demoting workflows that regress. Evaluated on a production cloud networking AIOps system processing tens of thousands of incidents per month, the approach increased deterministic execution from 0% to 45% over eight months, reduced per-incident agent costs by more than 70% despite doubling incident volume, and improved safety through greater reproducibility and auditability. The paper also presents the execution taxonomy, promotion and demotion criteria, trace extraction methodology, economic model, safety considerations, and discusses limitations and threats to validity.

Enhancing perceptual dimensions while miniaturizing imaging systems presents significant challenges for high-dimensional visual sensing. Conventionally, the acquisition of the 5D (x,y,u,v,λ) spectral light field (5D-SLF) data cube relies on bulky and expensive camera arrays, which are impractical for widespread application. Existing single-detector systems are fundamentally limited by a trade-off between the resolutions of different dimensions owing to insufficient coding capabilities. Here we introduce an Aperture-aware Dispersion Light-field Imaging Spectrometer (ADLIS), that targets a synergy between compactness and resolution through aperture-multiplexed modulation, leveraging the inherent spectral-filtering properties of birefringent material. Using only a manufacturing-friendly and cost-effective phase plate made of birefringent quartz crystal, the aperture of the proposed ADLIS enables compact angular-spectral encoding that is highly sensitive to both the incident angle and spectrum of incoming light. In contrast to the viewpoint-separation approach of microlens arrays, ADLIS employs aperture encoding to superimpose all viewpoints onto each sensor pixel. This shifts the design paradigm from spatial division to encoding integration, aiming to achieve full-resolution light field recovery. Thus, we develop the Aperture-aware Dispersion Light-field Imaging (ADLI) framework, which optimizes the aperture design and 5D-SLF reconstruction in an end-to-end (E2E) manner. Trained by simulation data and validated through real-world experiments, our system achieves robust high-performance 5D-SLF imaging while maintaining full spatial resolution.

The alignment of language models is typically studied through the lens of capability benchmarks, but the dynamics of how models change during post-training remain poorly understood. We argue that the physical sciences, and thermodynamic phase-transition theory in particular, offer a principled and underexplored vocabulary for reasoning about these dynamics. As a case study, we instantiate this position through the lens of material Crystallization, which is a well-studied thermodynamic phase transition. For tasks like random number generation, this breaks into 3 phases: (1) the high entropy liquid phase in the pretrained model, with many distinct sampling distributions promptable from the model; (2) the nucleation phase caused by supervised finetuning, in which behavior collapses onto a single seed distribution present in the pretrained LLM; and (3) a settling phase in which reinforcement learning techniques redistribute probability of the collapsed distribution, but largely keep it concentrated on the same options as the seed distribution. We propose intuitive metrics to verify the transitions between these phases, and validate the idea across a range of random tasks. Crystallization is one instance of a broader class of physical frameworks we believe alignment research should import to answer questions about where alignment-induced structure comes from, why it converges where it does, and what it fundamentally cannot change.

This project introduces the CRISTAL Method (Coherent Reliable Intentional Synthesis of Truthful Analysis Logic), a neurosymbolic framework for automating complex analysis workflows, with fundamental investment analysis as a primary use case. This domain poses major challenges: high structural uncertainty, noisy and subjective data, tight attention budgets, and the need for justified, reproducible decisions. Human analysts often struggle in this domain due to cognitive biases and limitations, suggesting significant value in automation. But while LLM-based agents have been proposed as analytical aids, their limitations -- poor numerical reasoning, unawareness of uncertainty, and lack of reproducibility -- hinder their effectiveness in this context. CRISTAL addresses these gaps through a principled blend of statistical model synthesis, continuous learning, and active learning. Starting from a natural-language prior knowledge curriculum, CRISTAL builds a dynamic, interpretable probabilistic program that enables full Bayesian inference, including uncertainty quantification and budget-aware data acquisition. CRISTAL continually refines its world model during analysis, leveraging LLMs for code synthesis and learning. We validate CRISTAL on a novel benchmark of synthetic equities with rich financial and textual data. On a company classification task, CRISTAL achieves Bayes-optimal accuracy with just 5 examples and a 5-second budget, outperforming state-of-the-art LLMs that plateau around 40% accuracy even with order-of-magnitude more input data and compute.

Predicting a material's properties from its structure is a central, fast-advancing problem in computational materials science. A decade of work has produced standard public benchmarks and many published machine-learning models for the task (Dunn et al., 2020). The task's fixed metric and these baselines make it a natural setting for autonomous agent research (Karpathy, 2026). On the MatBench band-gap benchmark ($>$100k crystals), a general-purpose coding agent autonomously built the most accurate model trained without external pretraining, ahead of all seventeen expert-designed models reported for the task. A closer analysis shows it reached this by implementing known methods: either already standard in crystal neural-network models, or borrowed from other areas of machine learning. The contributing implementations include element-pair features on each message-passing edge and a crystal space-group embedding. The work not only demonstrates that LLM-agent autonomous research can optimize an expert-designed machine learning model for material property prediction, but also investigates the limitations of such autonomous research.

Closed-loop materials discovery iterates between proposing candidate structures and evaluating their properties, and property evaluation dominates the cost. In the generative variant, a learned prior proposes candidate crystals and a property oracle scores them; we ask whether a cheap probabilistic surrogate can triage the generator's output, and what such a surrogate must do well. Across three architecturally distinct pretrained diffusion priors (MatterGen, CrystalFlow, ADiT) and two targets (room-temperature heat capacity and bulk modulus), we insert a Gaussian process acquisition gate between structure generation and the oracle in an RL-steered generative workflow. The gate matches or exceeds ungated fine-tuning of the generative model while capping oracle calls at a fixed per-cycle budget. Budget-matched ablations isolate the mechanism. At an identical four-call budget, ranking-based selection outperforms arbitrary selection, confirming that the gain comes from the surrogate's choice; the gate comes within $\sim$9% of exhaustive oracle spending at roughly one-fifth of the calls. A density-functional-theory check of the bulk-modulus discoveries confirms the learned oracle to within 2.5% on average and the surrogate's ranking of the generated structures at Spearman $ρ= 0.94$. A cross-factorial benchmark of surrogate performance spanning mechanical, electronic, and vibrational properties identifies pretrained ORB embeddings with a Gaussian process as the most reliable combination, which we adopt as the building blocks of the proposed workflow. The complete pipeline is released as open-source software.

There has been rapid progress in generative artificial intelligence (AI) models for inorganic crystal design, which can efficiently generate large numbers of candidate compounds after being trained on databases of known crystals. However, it remains unclear whether they genuinely expand the accessible materials search space beyond conventional strategies such as elemental substitution within known structure types. We address this question by developing a workflow to assess whether AI-generated crystals are duplicates of training structures, reproducible by elemental substitution, or unmatched by either criterion. Applying this workflow to representative generative models reveals that 81-92% of chemically valid and metastable generated crystals are either training duplicates or substitution-derived structures. This tendency is particularly strong in high-symmetry crystal systems, even though many possible structural prototypes remain unexplored. Further analysis of the underlying structural fingerprints shows that low-symmetry structures beyond duplication or substitution can be interpreted as interpolation in training-data-rich regions, while high-symmetry duplicates appear to result from memorisation in training-sparse regions. Our findings highlight a limitation in the current generation of models that exhibit a bias towards known structural prototypes in the high symmetry regions, but enable wider exploration of the low-symmetry structural space.

Machine-learned interatomic potentials now enable efficient atomistic evaluation for interactive materials discovery, yet closed-loop crystal search methods remain fragmented across bespoke pipelines for editing, relaxation, scoring, constraints, and bookkeeping. We introduce SciVerseGym, a Gymnasium-compatible environment for sequential crystal discovery that frames crystal design as a Markov decision process. Agents observe an atomistic structure, apply chemically meaningful edits, and receive feedback from a configurable evaluator. SciVerseGym supports local and global actions, including elemental substitution, lattice perturbation, atomic displacement, vacancy creation, and atom insertion, along with configurable chemical spaces, structure pools, atomistic and graph-based observations, custom rewards, optional relaxation, and stability or phonon-related diagnostics. Each step applies an edit, evaluates the candidate using a machine-learned interatomic potential or any ASE-compatible calculator, and returns the standard (obs, reward, terminated, truncated, info) tuple. By decoupling agent logic from materials infrastructure, SciVerseGym provides an open, reproducible, and extensible testbed for reinforcement learning, Bayesian optimization, evolutionary search, and language-agent workflows in closed-loop crystal discovery. Code is available at: https://github.com/Bin-Cao/SciVerseGym.

The emergence of Large Language Models (LLMs) has inspired the vision of generating bespoke crystal materials directly from natural-language instructions, enabling users to design materials through intuitive, conversational interaction. Existing text-to-crystal generative models represent important early steps toward this goal, but they suffer from two critical limitations: (i) restricted input formats that require highly structured descriptions (e.g., chemical formulas), and (ii) one-directional generation, where models can map text to crystal but cannot perform the inverse. These limitations prevent fully conversational workflows and hinder alignment with users' inherently ambiguous and evolving desiderata. We address these challenges with LapidaryEngine, the first model to support fully conversational crystal generation. LapidaryEngine accepts free-form natural-language requests and performs iterative refinement and editing in a dialogue-like manner. The key innovation is a pivot representation, a third, intermediate form that enables bidirectional translation between text and crystal structures despite the absence of direct paired datasets. Leveraging this pivot allows robust interpretation of user feedback and precise structural control. We demonstrate LapidaryEngine across diverse tasks, including insulator discovery, stability optimization, compositional modification, and structural editing, showcasing its ability to align generated materials with user intent in an interactive manner.

Understanding where LLMs store factual knowledge is critical for hallucination mitigation. We systematically quantify Late Crystallization: factual knowledge does not gradually emerge across layers but "crystallizes" abruptly at the final layers. Across five model families (Pythia, Gemma, Qwen2.5, Llama-3.1, Mistral; 0.5--14B), 26.8%--93.4% of correct answers never enter top-10 predictions at any intermediate layer, with late emergence (>80% depth) consistent across architectures. Cross-scale (Qwen2.5-14B) and cross-benchmark (MMLU: 98.2%) results confirm generality; tuned lens rules out probe artifacts. A sentiment-classification control (0.5% for Qwen vs. 85.9% factual; 2.0% for Mistral vs. 26.8%) confirms the phenomenon is specific to factual recall. Late Crystallization yields a crystallization-guided intervention principle: CAA outperforms DoLa on moderate-crystallization models (Llama, Mistral; p<0.001), with a directionally consistent reversal on high-crystallization Qwen (+25.4% vs. +15.5% MC1, p=0.069). LayerNorm ablation shows crystallization is intrinsic to the residual stream; LN scaling (x1.2) yields +11.8% MC1 with zero inference overhead. We further reveal a Computability-Memorization Spectrum: computable knowledge crystallizes earlier (layer 22.1/28) than memorized facts (28.0/28). We release MechLens supporting five model families.

Fast and accurate prediction of crystal properties is a central challenge in new materials design. Graph neural networks and Transformer-based models have emerged as powerful tools for this task due to their ability to encode the local structural environment of atoms within a crystal. However, these models are data-hungry, and in practice, labeled data for crystal properties are scarce. Pretraining-finetuning strategies, particularly those based on diffusion models, have shown promise in addressing these limitations. In this work, we introduce a novel latent diffusion based pretraining framework, CrysLDNet, designed to mitigate data scarcity. Our approach integrates a Variational Autoencoder (VAE) with a diffusion model during the pretraining stage. The VAE encoder maps 3D crystal structures into a smooth latent space within which the diffusion process is applied. This latent diffusion pretraining enables the graph encoder to effectively capture structural and chemical semantics from large-scale unlabeled data, which can then be finetuned for specific property prediction tasks. Comprehensive experiments on popular DFT datasets for property prediction reveal that CrysLDNet significantly outperforms both training-from-scratch and pretrained baselines, with improvements of 4.26% and 4.90% on the JARVIS and MP datasets, respectively. Additionally, the learned representations remain robust in sparse-data conditions and are expressive enough to correct DFT errors when finetuned with limited experimental data. Code is available at: https://github.com/shrimonmuke0202/CrysLDNet.git.

De novo crystal generation, a central task in materials discovery, aims to generate crystals that are simultaneously valid, stable, unique, and novel. Existing methods mainly rely on black-box stochastic sampling, providing limited control over how generated structures move beyond the observed distribution. In this paper, we introduce a concept-based compositional framework for crystal generation. We train a vector-quantized variational autoencoder to automatically discover a shared set of reusable crystal concepts, which serve as building blocks for guided generation. These learned concepts naturally exhibit interpretability from both local atomic environments and global symmetry patterns, and generalize to crystals from different distributions. By recombining such concepts, our framework enables controllable exploration of novel crystals beyond the training distribution, rather than relying solely on unconstrained random sampling. To further improve composition efficiency, we introduce a composition generator and iteratively refine it using high-quality samples generated by the model itself. The resulting concept compositions are then used to condition downstream crystal generation. Numerical experiments on MP-20 and Alex-MP-20 show that compositing concepts separately increase base model up to 53.2% and 51.7% on V.S.U.N metric, with particular gains in novelty.

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 generative models mainly learn what stable crystals look like, with little explicit supervision for what makes them stable. We reveal a substantial representation gap between state-of-the-art crystal generative models and pretrained universal machine learning interatomic potentials (MLIPs) via energy probing, and show this gap can be closed by a simple training-time alignment. We propose Crystal REPresentation Alignment (CrystalREPA), a plug-and-play framework that aligns the atom-wise hidden states of generative encoders with frozen MLIP representations through an element-aware contrastive objective, transferring stability-aware atomistic priors with marginal training overhead and no additional inference cost. Across three generative frameworks, ten MLIP teachers, and two benchmark datasets, CrystalREPA consistently improves the thermodynamic stability, structural validity, and structural fidelity of generated crystals. Equally important, we find that an MLIP's transfer effectiveness is poorly predicted by its accuracy on standard leaderboards (e.g., Matbench Discovery) but strongly predicted by the distinguishability of its atom-wise representation space, yielding a practical, accuracy-independent criterion for selecting MLIP teachers for generative transfer.

Crystal generative models have shown rapid progress for accelerating the discovery of bulk, periodic materials. However, many material systems such as 2D superconductors, thin film semiconductors, and catalytic surfaces are diperiodic, i.e., aperiodic along one of the lattice directions. These systems are invariant under the layer groups, which are known to influence materials properties yet not considered by existing models. In this paper, we propose SLayerGen, a generative model that produces crystals constrained to be invariant to any space or layer group. SLayerGen consists of coarse-to-fine discrete autoregressive lattice generation; transformer-based autoregressive sampling of Wyckoff positions, elements, and numbers of symmetrically unique atoms; and space or layer group equivariant diffusion of atomic coordinates. For the diffusion component, we corrected an inconsistency in the loss from prior work arising from hexagonal groups being non-orthogonal in fractional coordinates. To facilitate progress in generative modeling of diperiodic materials, we assembled and filtered datasets of monolayers and bilayers, propose relevant evaluation metrics, and developed novel representations for layer group symmetries. For de novo generation of diperiodic materials, SLayerGen achieves consistent performance gains over bulk crystal generative models and is competitive when training jointly on bulk and diperiodic materials.

While machine-learned interatomic potentials (MLIPs) accelerate phonon dispersion calculations, merely identifying dynamical instabilities in computationally predicted materials is insufficient; automated pathways to resolve them are required. We introduce VibroML, an open-source Python toolkit driven by foundational MLIPs that shifts the paradigm from stability verification to automated structural remediation. VibroML employs an energy-guided genetic algorithm that vastly outperforms traditional soft-mode following, efficiently navigating the potential energy surface to uncover diverse, dynamically stable polymorphs. As 0 K harmonic stability does not guarantee macroscopic viability, an automated molecular dynamics workflow evaluates finite-temperature structural retention. VibroML also couples with ProtoCSP, our combinatorial structure prediction engine, to stabilize frustrated crystal topologies via targeted alloying, successfully rescuing functional perovskite networks like Cs$_2$KInI$_6$ and KTaSe$_3$. Demonstrating broader applicability, we mined the Alexandria database -- where ~50% of quaternary and 99.5% of quinary elemental combinations lack any structural entries -- to identify thousands of abandoned, high-symmetry stoichiometries. Deploying ProtoCSP's "cold start" retrieval and VibroML's evolutionary search on a sample, we successfully identified dynamically stable low-symmetry candidates. Through integrated structural remediation, thermal validation, and systematic compositional exploration, VibroML enables a comprehensive deep-screening approach, yielding physically sound structural propositions that far surpass standard high-throughput workflows.

Crystalline materials are widely used in technological applications, yet their discovery remains a significant challenge. As their properties are driven by structure, crystal structure prediction (CSP) methods play a central role in computational approaches aiming to accelerate this process. Previously, CSP has been approached from a combinatorial optimization perspective, with the core challenge of allocating atoms on a fine grid of predefined discrete positions within a unit cell while minimizing their interaction energy. Exact mathematical optimization methods provide guaranteed solutions, but they become computationally expensive for large-scale instances, where the atomic configuration space grows rapidly, particularly in the absence of additional symmetry constraints. In this work, we introduce a neural combinatorial optimization approach to the atom allocation challenge and, subsequently, CSP, based on graph neural networks (GNNs), which can effectively sample from the distribution of feasible structures in an unsupervised manner. We leverage expander graphs to construct computational graphs over discrete positions that capture both short- and long-range interactions between atoms, and employ the Gumbel-Sinkhorn approach to enforce the desired stoichiometry of the generated structures. We demonstrate that our method outperforms classical heuristic approaches and is competitive with a commercial optimization solver across a range of chemical compositions. This enables the use of ever-expanding GPU infrastructure to tackle the inherent combinatorial challenges of CSP, paving the way for scaling beyond current capabilities.

High-entropy alloys (HEAs) have attracted growing attention for their exceptional mechanical and thermal properties arising from complex atomic configurations. In this paper, we propose crystal fractional graph neural network for predicting the energy of high-entropy alloys by explicitly integrating both local atomic environments and global compositional information. The model consists of three components: a crystal graph neural network, which employs graph attention network layers to learn local interactions among 16 on-site atoms within the crystal lattice; fractional neural network, a fully connected network that embeds the global fraction of constituent elements; and feature fusion neural network, which fuses the outputs of the two submodels to predict the total crystal energy. We train the model on a dataset of 1,049 crystal structures and validate it on 198 quaternary structures, optimizing all hyperparameters via Optuna. Our results show that our model achieves an RMSE comparable to first-principles calculations and maintains high accuracy even for low-energy configurations. However, the model exhibits limitations in handling large crystal cells, which we aim to address in future work to extend its applicability to more complex systems.

Simulations of crystal growth are performed by using Convolutional Recurrent Neural Network surrogate models, trained on a dataset of time sequences computed by numerical integration of Allen-Cahn dynamics including faceting via kinetic anisotropy. Two network architectures are developed to take into account the effects of a variable supersaturation value. The first infers it implicitly by processing an input mini-sequence of a few evolution frames and then returns a consistent continuation of the evolution. The second takes the supersaturation parameter as an explicit input along with a single initial frame and predicts the entire sequence. The two models are systematically tested to establish strengths and weaknesses, comparing the prediction performance for models trained on datasets of different size and, in the first architecture, different lengths of input mini-sequence. The analysis of point-wise and mean absolute errors shows how the explicit parameter conditioning guarantees the best results, reproducing with high-fidelity the ground-truth profiles. Comparable results are achievable by the mini-sequence approach only when using larger training datasets. The trained models show strong conditioning by the supersaturation parameter, consistently reproducing its overall impact on growth rates as well as its local effect on the faceted morphology. Moreover, they are perfectly scalable even on 256 times larger domains and can be successfully extended to more than 10 times longer sequences with limited error accumulation. The analysis highlights the potential and limits of these approaches in view of their general exploitation for crystal growth simulations.

Generative diffusion models have emerged as powerful tools for the discovery of inorganic crystal structures, yet steering their sampling process toward user-defined physical and chemical objectives remains challenging. We present a computational framework that integrates adaptive constraint guidance into a pre-trained crystal diffusion model, enabling the generation of candidate structures that satisfy targeted structural and chemical requirements without model retraining. The approach incorporates differentiable constraint functions directly during sampling, providing an interpretable mechanism for expert-driven exploration of the crystal structure space. To assess the reliability of generated candidates, we introduce a multi-stage validation workflow combining descriptor-based analysis, duplicate removal, comparison with reference crystal databases, graph neural network energy prediction, and thermodynamic stability evaluation through convex-hull analysis. The framework is applied to several classes of inorganic compounds and to constraints involving atomic volume, local coordination environments, and near-neighbor structural motifs. Results demonstrate that adaptive guidance effectively redirects the sampling distribution toward structures exhibiting the desired characteristics while preserving chemical plausibility. Subsequent validation reveals which generated candidates remain viable after energetic and thermodynamic screening. The proposed methodology provides a practical and transparent strategy for incorporating expert knowledge into crystal generative models and establishes a general computational framework for constrained materials discovery.

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.