Polymorphism, the ability of a compound to crystallize in multiple distinct structures, plays a vital role in determining the physical, chemical, and functional properties of polymorphic materials. While polymorphism enables many critical crystalline materials applications with special properties, predicting such polymorphic structures remains a big challenge. In this study, we analyze structural variations in the Materials Project database, including metastable and pressure-stabilized crystal structures, to explore the topological landscape of polymorphism. Using topological analysis, we identify key statistical patterns in composition, space-group distributions, and polyhedral building blocks. We discover that frequent space group pairs, such as (71,225), display consistent topological patterns across different compounds. We further show that, local polyhedral environments are often conserved across diverse structural variants of a given formula, even as global symmetry and packing arrangements change. By embedding these structures into a topological vector space, we show that structures can cluster together independent of their space group labels. Validation against experimental data from the ICSD confirms that these trends are physically real and not computational artifacts. These findings establish local topological identity as a more robust descriptor than space group symmetry for predicting and classifying structural diversity in inorganic polymorphic systems.

Crystal structure prediction remains a major challenge in materials science, directly impacting the discovery and development of next-generation materials. We introduce Template-based Crystal Structure Prediction (TCSP) 2.0, a substantial evolution of our framework that advances predictive capabilities through synergistic integration of several key techniques into its major components. Building upon TCSP 1.0’s template-matching foundation, this enhanced version implements three critical innovations: (1) replacement of Pymatgen with deep learning-based BERTOS model for oxidation state prediction with superior performance, (2) implementation of sophisticated element embedding distance metrics for improved chemical similarity assessment, and (3) development of a robust majority voting mechanism for space group selection that reduces prediction uncertainty. TCSP 2.0 also expands its template base by incorporating template structures from Materials Cloud, C2DB, and GNoME databases alongside the original Materials Project repository, creating a more comprehensive structural foundation. Rigorous validation across 180 diverse test cases of the CSPBenchmark demonstrates TCSP 2.0’s exceptional performance, achieving 64.44% consensus success rate for top-1 predictions, substantially outperforming both its predecessor (22.78%) and the machine learning template based CSPML (46.84%) while shadowing the performance of deep learning based EquiCSP (62.22%). The related open-source code can be accessed freely at https://github.com/usccolumbia/TCSP.

Foundation models (FMs) have recently shown remarkable in-context learning (ICL) capabilities across diverse scientific domains. In this work, we introduce a unified in-context learning foundation model (ICL-FM) framework for materials property prediction that integrates both composition-based and structure-aware representations. The proposed approach couples the pretrained TabPFN transformer with graph neural network (GNN)-derived embeddings and our novel MagpieEX descriptors. MagpieEX augments traditional features with cation-anion interaction data to explicitly measure bond ionicity and charge-transfer asymmetry, capturing interatomic bonding characteristics that influence vibrational and thermal transport properties. Comprehensive experiments on the MatBench benchmark suite and a standalone lattice thermal conductivity (LTC) dataset demonstrate that ICL-FM achieves competitive or superior performance to state-of-the-art (SOTA) models with significantly reduced training costs. Remarkably, the training-free ICL-FM outperformed sophisticated SOTA GNN models in five out of six representative composition-based tasks, including a significant 9.93% improvement in phonon frequency prediction. On the LTC dataset, the FM effectively models complex phenomena such as phonon-phonon scattering and atomic mass contrast. t-SNE analysis reveals that the FM acts as a physics-aware feature refiner, transforming raw, disjoint feature clusters into continuous manifolds with gradual property transitions. This restructured latent space enhances interpolative prediction accuracy while aligning learned representations with underlying physical laws. This study establishes ICL-FM as a generalizable, data-efficient paradigm for materials informatics.

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

Crystalline materials can form different structural arrangements (i.e., polymorphs) with the same chemical composition, exhibiting distinct physical properties depending on how they are synthesized or the conditions under which they operate. For example, carbon can exist as graphite (soft, conductive) or diamond (hard, insulating). Computational methods that can predict these polymorphs are vital in materials science, which help understand stability relationships, guide synthesis efforts, and discover new materials with desired properties without extensive trial-and-error experimentation. However, effective crystal structure prediction (CSP) algorithms for inorganic polymorph structures remain limited. ParetoCSP2 is proposed, a multi-objective genetic algorithm for polymorphism CSP that incorporates an adaptive space group diversity control technique and the sustainable age-fitness Pareto optimized evolutionary mechanism, preventing over-representation of any single space group in the population guided by a neural network interatomic potential. Using an improved population initialization method and performing iterative structure relaxation, ParetoCSP2 not only alleviates premature convergence but also achieves improved convergence speed. These results show that ParetoCSP2 achieves excellent performance in polymorphism prediction, including a nearly perfect space group and structural similarity accuracy for formulas with two polymorphs but with the same number of unit cell atoms. Evaluated on a benchmark dataset, it outperforms baseline algorithms by factors of 2.46-8.62 for these accuracies and improves by 44.8-87.04% across key performance metrics for regular CSP. This source code is freely available at https://github.com/usccolumbia/ParetoCSP2.

Crystals are essential constituents of a wide range of materials, encompassing both advanced technologies and everyday applications. Recently, deep learning-based methods for crystal property prediction have demonstrated remarkable performance, greatly facilitating the discovery of novel materials. However, these approaches typically concentrate on atom-wise interactions and often fail to account for periodicity, a fundamental characteristic of crystals. To address this limitation, we propose a novel plug-and-play component, the Periodicity Injection Module (PIM), which seamlessly incorporates periodicity into existing crystal models. Specifically, the PIM employs crystal-wise attention to ensure that the surroundings of unit cells at periodic distances remain identical, aligning with the definition of crystal periodicity. By capturing interactions among bases at the crystal level, the PIM complements and enhances the modeling of intra-crystal interactions. Extensive experiments on benchmark datasets demonstrate that our PIM significantly improves crystal property prediction.

Computational materials discovery is limited by the high cost of first-principles calculations. Machine learning (ML) potentials that predict energies from crystal structures are promising, but existing methods face computational bottlenecks. Steerable graph neural networks (GNNs) encode geometry with spherical harmonics, respecting atomic symmetries – permutation, rotation, and translation – for physically realistic predictions. Yet maintaining equivariance is difficult: activation functions must be modified, and each layer must handle multiple data types for different harmonic orders. We present Facet, a GNN architecture for efficient ML potentials, developed through systematic analysis of steerable GNNs. Our innovations include replacing expensive multi-layer perceptrons (MLPs) for interatomic distances with splines, which match performance while cutting computational and memory demands. We also introduce a general-purpose equivariant layer that mixes node information via spherical grid projection followed by standard MLPs – faster than tensor products and more expressive than linear or gate layers. On the MPTrj dataset, Facet matches leading models with far fewer parameters and under 10

Crystal structure prediction (CSP) is now increasingly used in the discovery of novel materials with applications in diverse industries. However, despite decades of developments, the problem is far from being solved. With the progress of deep learning, search algorithms, and surrogate energy models, there is a great opportunity for breakthroughs in this area. However, the evaluation of CSP algorithms primarily relies on manual structural and formation energy comparisons. The lack of a set of well-defined quantitative performance metrics for CSP algorithms makes it difficult to evaluate the status of the field and identify the strengths and weaknesses of different CSP algorithms. Here, we analyze the quality evaluation issue in CSP and propose a set of quantitative structure similarity metrics, which when combined can be used to automatically determine the quality of the predicted crystal structures compared to the ground states. Our CSP performance metrics can then be utilized to evaluate the large set of existing and emerging CSP algorithms, thereby alleviating the burden of manual inspection on a case -by -case basis. The related open -source code can be accessed freely at https://github.com/usccolumbia/CSPBenchMetrics.

Computational prediction of stable crystal structures has a profound impact on the large-scale discovery of novel functional materials. However, predicting the crystal structure solely from a material's composition or formula is a promising yet challenging task, as traditional ab initio crystal structure prediction (CSP) methods rely on time-consuming global searches and first-principles free energy calculations. Inspired by the recent success of deep learning approaches in protein structure prediction, which utilize pairwise amino acid interactions to describe 3D structures, we present AlphaCrystal-II, a novel knowledge-based solution that exploits the abundant inter-atomic interaction patterns found in existing known crystal structures. AlphaCrystal-II predicts the atomic distance matrix of a target crystal material and employs this matrix to reconstruct its 3D crystal structure. By leveraging the wealth of inter-atomic relationships of known crystal structures, our approach demonstrates remarkable effectiveness and reliability in structure prediction through comprehensive experiments. This work highlights the potential of data-driven methods in accelerating the discovery and design of new materials with tailored properties.

Crystal structure prediction (CSP) is now increasingly used in discovering novel materials with applications in diverse industries. However, despite decades of developments and significant progress in this area, there lacks a set of well-defined benchmark dataset, quantitative performance metrics, and studies that evaluate the status of the field. We aim to fill this gap by introducing a CSP benchmark suite with 180 test structures along with our recently implemented CSP performance metric set. We benchmark a collection of 13 state-of-the-art (SOTA) CSP algorithms including template-based CSP algorithms, conventional CSP algorithms based on DFT calculations and global search such as CALYPSO, CSP algorithms based on machine learning (ML) potentials and global search, and distance matrix based CSP algorithms. Our results demonstrate that the performance of the current CSP algorithms is far from being satisfactory. Most algorithms cannot even identify the structures with the correct space groups except for the template-based algorithms when applied to test structures with similar templates. We also find that the ML potential based CSP algorithms are now able to achieve competitive performances compared to the DFT-based algorithms. These CSP algorithms' performance is strongly determined by the quality of the neural potentials as well as the global optimization algorithms. Our benchmark suite comes with a comprehensive open-source codebase and 180 well-selected benchmark crystal structures, making it convenient to evaluate the advantages and disadvantages of CSP algorithms from future studies. All the code and benchmark data are available at https://github.com/usccolumbia/cspbenchmark

Self-supervised neural language models have recently achieved unprecedented success, from natural language processing to learning the languages of biological sequences and organic molecules. These models have demonstrated superior performance in the generation, structure classification, and functional predictions for proteins and molecules with learned representations. However, most of the masking-based pre-trained language models are not designed for generative design, and their black-box nature makes it difficult to interpret their design logic. Here we propose BLMM Crystal Transformer, a neural network based probabilistic generative model for generative and tinkering design of inorganic materials. Our model is built on the blank filling language model for text generation and has demonstrated unique advantages in learning the "materials grammars" together with high-quality generation, interpretability, and data efficiency. It can generate chemically valid materials compositions with as high as 89.7\% charge neutrality and 84.8\% balanced electronegativity, which are more than 4 and 8 times higher compared to a pseudo random sampling baseline. The probabilistic generation process of BLMM allows it to recommend tinkering operations based on learned materials chemistry and makes it useful for materials doping. Combined with the TCSP crysal structure prediction algorithm, We have applied our model to discover a set of new materials as validated using DFT calculations. Our work thus brings the unsupervised transformer language models based generative artificial intelligence to inorganic materials. A user-friendly web app has been developed for computational materials doping and can be accessed freely at \url{www.materialsatlas.org/blmtinker}.

While crystal structure prediction (CSP) remains a longstanding challenge, we introduce ParetoCSP, a novel algorithm for CSP, which combines a multi-objective genetic algorithm (MOGA) with a neural network inter-atomic potential (IAP) model to find energetically optimal crystal structures given chemical compositions. We enhance the NSGA-III algorithm by incorporating the genotypic age as an independent optimization criterion and employ the M3GNet universal IAP to guide the GA search. Compared to GN-OA, a state-of-the-art neural potential based CSP algorithm, ParetoCSP demonstrated significantly better predictive capabilities, outperforming by a factor of $2.562$ across $55$ diverse benchmark structures, as evaluated by seven performance metrics. Trajectory analysis of the traversed structures of all algorithms shows that ParetoCSP generated more valid structures than other algorithms, which helped guide the GA to search more effectively for the optimal structures

Deep learning models have been widely used for high-performance material property prediction. However, training such models usually requires a large amount of labeled data, which are usually unavailable. Self-supervised learning (SSL) methods have been proposed to address this data scarcity issue. Herein, we present DSSL, a physics-guided dual SSL framework, for graph neural network-based material property prediction, which combines node masking-based generative SSL with atomic coordinate perturbation-based contrastive SSL strategies to capture local and global information about input crystals. Moreover, we achieve physics-guided pretraining by using the macroproperty (e.g., elasticity)-related microproperty prediction of atomic stiffness as an additional pretext task. We pretrain our DSSL model on the Materials Project database and fine-tune it with 10 material property data sets. The experimental results demonstrate that teaching neural networks some physics using the SSL strategy can afford ≤26.89% performance improvement compared to that of the baseline models.

Self-supervised neural language models have recently found wide applications in the generative design of organic molecules and protein sequences as well as representation learning for downstream structure classification and functional prediction. However, most of the existing deep learning models for molecule design usually require a big dataset and have a black-box architecture, which makes it difficult to interpret their design logic. Here we propose the Generative Molecular Transformer (GMTransformer), a probabilistic neural network model for generative design of molecules. Our model is built on the blank filling language model originally developed for text processing, which has demonstrated unique advantages in learning the “molecules grammars” with high-quality generation, interpretability, and data efficiency. Benchmarked on the MOSES datasets, our models achieve high novelty and Scaf compared to other baselines. The probabilistic generation steps have the potential in tinkering with molecule design due to their capability of recommending how to modify existing molecules with explanation, guided by the learned implicit molecule chemistry. The source code and datasets can be accessed freely at https://github.com/usccolumbia/GMTransformer

Understanding materials' composition-structure-function relationships is of critical importance for the design and discovery of novel functional materials. While most such studies focus on individual materials, we conducted a global mapping study of all known materials deposited in the Materials Project database to investigate their distributions in the space of a set of seven compositional, structural, physical, and neural latent descriptors. These two-dimensional materials maps along with their density maps allow us to illustrate the distribution of the patterns and clusters of different shapes, which indicates the propensity of these materials and the tinkering history of existing materials. We then overlap the material properties such as composition prototypes and piezoelectric properties over the background material maps to study the relationships of how material compositions and structures affect their physical properties. We also use these maps to study the spatial distributions of properties of known inorganic materials, in particular those of local vicinities in structural space such as structural density and functional diversity. These maps provide a uniquely comprehensive overview of materials and space and thus reveal previously undescribed fundamental properties. Our methodology can be easily extended by other researchers to generate their own global material maps with different background maps and overlap properties for both distribution understanding and cluster-based new material discovery. The source code for feature generation and generated maps is available at https://github.com/usccolumbia/matglobalmapping.

Pre-trained transformer language models (LMs) on large unlabeled corpus have produced state-of-the-art results in natural language processing, organic molecule design, and protein sequence generation. However, no such models have been applied to learn the composition patterns for the generative design of material compositions. Here we train a series of seven modern transformer models (GPT, GPT-2, GPT-Neo, GPT-J, BLMM, BART, and RoBERTa) for materials design using the expanded formulas of the ICSD, OQMD, and Materials Projects databases. Six different datasets with/out non-charge-neutral or EB samples are used to benchmark the generative design performances and uncover the biases of modern transformer models for the generative design of materials compositions. Our experiments show that the materials transformers based on causal LMs can generate chemically valid material compositions with as high as 97.61% to be charge neutral and 91.22% to be electronegativity balanced, which has more than six times higher enrichment compared to the baseline pseudo-random sampling algorithm. Our LMs also demonstrate high generation novelty and their potential in new materials discovery is proved by their capability to recover the leave-out materials. We also find that the properties of the generated compositions can be tailored by training the models with selected training sets such as high-bandgap samples. Our experiments also show that different models each have their own preference in terms of the properties of the generated samples and their running time complexity varies a lot. We have applied our materials transformers to discover a set of new materials as validated using density functional theory calculations. All our trained materials transformer models and code can be accessed freely at http://www.github.com/usccolumbia/MTransformer .

Evolutionary machine learning (EML) has been increasingly applied to solving diverse science and engineering problems due to the global search, optimization, and multi-objective optimization capabilities of evolutionary algorithms and the strong modeling capability of complex functions and processes by machine learning (ML) and especially deep neural network models. They are widely used to solve modeling, prediction, control, and pattern detectionPattern detection problems. Especially EML algorithms are used for solving inverse designInverse design problems ranging from neural network architecture search, inverse materials design, control system design, and discoveryMaterials discovery of differential equations.

One of the long-standing problems in materials science is how to predict a material's structure and then its properties given only its composition. Experimental characterization of crystal structures has been widely used for structure determination, which is, however, too expensive for high-throughput screening. At the same time, directly predicting crystal structures from compositions remains a challenging unsolved problem. Herein we propose a deep learning algorithm for predicting the XRD spectrum given only the composition of a material, which can then be used to infer key structural features for downstream structural analysis such as crystal system or space group classification or crystal lattice parameter determination or materials property prediction. Benchmark studies on two data sets show that our DeepXRD algorithm can achieve good performance for XRD prediction as evaluated over our test sets. It can thus be used in high-throughput screening in the huge materials composition space for materials discovery.

Pre-trained transformer language models on large unlabeled corpus have produced state-of-the-art results in natural language processing, organic molecule design, and protein sequence generation. However, no such models have been applied to learn the composition patterns of inorganic materials. Here we train a series of seven modern transformer language models (GPT, GPT-2, GPT-Neo, GPT-J, BLMM, BART, and RoBERTa) using the expanded formulas from material deposited in the ICSD, OQMD, and Materials Projects databases. Six different datasets with/out non-charge-neutral or balanced electronegativity samples are used to benchmark the performances and uncover the generation biases of modern transformer models for the generative design of materials compositions. Our extensive experiments showed that the causal language models based materials transformers can generate chemically valid materials compositions with as high as 97.54\% to be charge neutral and 91.40\% to be electronegativity balanced, which has more than 6 times higher enrichment compared to a baseline pseudo-random sampling algorithm. These models also demonstrate high novelty and their potential in new materials discovery has been proved by their capability to recover the leave-out materials. We also find that the properties of the generated samples can be tailored by training the models with selected training sets such as high-bandgap materials. Our experiments also showed that different models each have their own preference in terms of the properties of the generated samples and their running time complexity varies a lot. We have applied our materials transformer models to discover a set of new materials as validated using DFT calculations.

The availability and easy access of large-scale experimental and computational materials data have enabled the emergence of accelerated development of algorithms and models for materials property prediction, structure prediction, and generative design of materials. However, the lack of user-friendly materials informatics web servers has severely constrained the wide adoption of such tools in the daily practice of materials screening, tinkering, and design space exploration by materials scientists. Herein we first survey current materials informatics web apps and then propose and develop MaterialsAtlas.org, a web-based materials informatics toolbox for materials discovery, which includes a variety of routinely needed tools for exploratory materials discovery, including material’s composition and structure validity check (e.g. charge neutrality, electronegativity balance, dynamic stability, Pauling rules), materials property prediction (e.g. band gap, elastic moduli, hardness, and thermal conductivity), search for hypothetical materials, and utility tools. These user-friendly tools can be freely accessed at http://www.materialsatlas.org . We argue that such materials informatics apps should be widely developed by the community to speed up materials discovery processes.