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The accurate prediction of material properties is crucial in a wide range of scientific and engineering disciplines. Machine learning (ML) has advanced the state of the art in this field, enabling scientists to discover novel materials and design materials with specific desired properties. However, one major challenge that persists in material property prediction is the generalization of models to out-of-distribution (OOD) samples,i.e., samples that differ significantly from those encountered during training. In this paper, we explore the application of advancements in OOD learning approaches to enhance the robustness and reliability of material property prediction models. We propose and apply the Crystal Adversarial Learning (CAL) algorithm for OOD materials property prediction,which generates synthetic data during training to bias the training towards those samples with high prediction uncertainty. We further propose an adversarial learning based targeting finetuning approach to make the model adapted to a particular OOD dataset, as an alternative to traditional fine-tuning. Our experiments demonstrate the success of our CAL algorithm with its high effectiveness in ML with limited samples which commonly occurs in materials science. Our work represents a promising direction toward better OOD learning and materials property prediction.

Deep learning (DL) models have been widely used in materials property prediction with great success, especially for properties with large datasets. However, the out-of-distribution (OOD) performances of such models are questionable, especially when the training set is not large enough. Here we showed that using physical encoding rather than the widely used one-hot encoding can significantly improve the OOD performance by increasing the models' generalization performance, which is especially true for models trained with small datasets. Our benchmark results of both composition- and structure-based deep learning models over six datasets including formation energy, band gap, refractive index, and elastic properties predictions demonstrated the importance of physical encoding to OOD generalization for models trained on small datasets.

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, Comment: 26 pages

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., Comment: 16 pages

Deep learning (DL) models have now been widely used for high-performance material property prediction for properties such as formation energy and band gap. However, training such DL models usually requires a large amount of labeled data, which is usually not available for most materials properties such as exfoliation energy and elastic properties. Self-supervised learning (SSL) methods have been proposed to address this data scarcity issue by learning inherent representations from unlabeled data in various research fields. Herein, we present DSSL, a physics-guided Dual SSL framework, for graph neural networks (GNNs) based material property prediction. This hybrid framework combines node-masking based predictive SSL with atomic coordinate perturbation based contrastive SSL strategies, allowing it to learn structural embeddings that capture both local and global information of input crystals. Especially, we propose to use predicting the macroproperty (e.g. elasticity) related microproperty such as atomic stiffness as an additional pretext task to achieve physics-guided pretraining process. We pretrain our DSSL model on the Materials Project database with unlabeled data and finetune it with ten extra datasets with different material properties. The experimental results demonstrate that teaching neural networks some physics using the SSL strategy can bring up to 26.89\% performance improvement compared to the baseline GNN models. Our source code is now freely available at https://github.com/usccolumbia/DSSL, Comment: 11 pages

Photon counting radiation detectors have become an integral part of medical imaging modalities such as Positron Emission Tomography or Computed Tomography. One of the most promising detectors is the wide bandgap room temperature semiconductor detectors, which depends on the interaction gamma/x-ray photons with the detector material involves Compton scattering which leads to multiple interaction photon events (MIPEs) of a single photon. For semiconductor detectors like CdZnTeSe (CZTS), which have a high overlap of detected energies between Compton and photoelectric events, it is nearly impossible to distinguish between Compton scattered events from photoelectric events using conventional readout electronics or signal processing algorithms. Herein, we report a deep learning classifier CoPhNet that distinguishes between Compton scattering and photoelectric interactions of gamma/x-ray photons with CdZnTeSe (CZTS) semiconductor detectors. Our CoPhNet model was trained using simulated data to resemble actual CZTS detector pulses and validated using both simulated and experimental data. These results demonstrated that our CoPhNet model can achieve high classification accuracy over the simulated test set. It also holds its performance robustness under operating parameter shifts such as Signal-Noise-Ratio (SNR) and incident energy. Our work thus laid solid foundation for developing next-generation high energy gamma-rays detectors for better biomedical imaging., Comment: 17 pages

Due to the vast chemical space, discovering materials with a specific function is challenging. Chemical formulas are obligated to conform to a set of exacting criteria such as charge neutrality, balanced electronegativity, synthesizability, and mechanical stability. In response to this formidable task, we introduce a deep learning-based generative model for material composition and structure design by learning and exploiting explicit and implicit chemical knowledge. Our pipeline first uses deep diffusion language models as the generator of compositions and then applies a template-based crystal structure prediction algorithm to predict their corresponding structures, which is then followed by structure relaxation using a universal graph neural network-based potential. The density functional theory (DFT) calculations of the formation energies and energy-above-the-hull analysis are used to validate new structures generated through our pipeline. Based on the DFT calculation results, six new materials, including Ti2HfO5, TaNbP, YMoN2, TaReO4, HfTiO2, and HfMnO2, with formation energy less than zero have been found. Remarkably, among these, four materials, namely Ti2$HfO5, TaNbP, YMoN2, and TaReO4, exhibit an e-above-hull energy of less than 0.3 eV. These findings have proved the effectiveness of our approach.

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

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 make 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 truths. Our CSP performance metrics can be then 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, Comment: 17 pages

Materials datasets are usually featured by the existence of many redundant (highly similar) materials due to the tinkering material design practice over the history of materials research. For example, the materials project database has many perovskite cubic structure materials similar to SrTiO$_3$. This sample redundancy within the dataset makes the random splitting of machine learning model evaluation to fail so that the ML models tend to achieve over-estimated predictive performance which is misleading for the materials science community. This issue is well known in the field of bioinformatics for protein function prediction, in which a redundancy reduction procedure (CD-Hit) is always applied to reduce the sample redundancy by ensuring no pair of samples has a sequence similarity greater than a given threshold. This paper surveys the overestimated ML performance in the literature for both composition based and structure based material property prediction. We then propose a material dataset redundancy reduction algorithm called MD-HIT and evaluate it with several composition and structure based distance threshold sfor reducing data set sample redundancy. We show that with this control, the predicted performance tends to better reflect their true prediction capability. Our MD-hit code can be freely accessed at https://github.com/usccolumbia/MD-HIT, Comment: 12pages

Understanding material 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 Material 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 materials 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 are available at https://github.com/usccolumbia/matglobalmapping, Comment: 17 pages

Two-dimensional (2D) materials have wide applications in superconductors, quantum, and topological materials. However, their rational design is not well established, and currently less than 6,000 experimentally synthesized 2D materials have been reported. Recently, deep learning, data-mining, and density functional theory (DFT)-based high-throughput calculations are widely performed to discover potential new materials for diverse applications. Here we propose a generative material design pipeline, namely material transformer generator(MTG), for large-scale discovery of hypothetical 2D materials. We train two 2D materials composition generators using self-learning neural language models based on Transformers with and without transfer learning. The models are then used to generate a large number of candidate 2D compositions, which are fed to known 2D materials templates for crystal structure prediction. Next, we performed DFT computations to study their thermodynamic stability based on energy-above-hull and formation energy. We report four new DFT-verified stable 2D materials with zero e-above-hull energies, including NiCl$_4$, IrSBr, CuBr$_3$, and CoBrCl. Our work thus demonstrates the potential of our MTG generative materials design pipeline in the discovery of novel 2D materials and other functional materials., Comment: 16 pages

Oxidation states are the charges of atoms after their ionic approximation of their bonds, which have been widely used in charge-neutrality verification, crystal structure determination, and reaction estimation. Currently only heuristic rules exist for guessing the oxidation states of a given compound with many exceptions. Recent work has developed machine learning models based on heuristic structural features for predicting the oxidation states of metal ions. However, composition based oxidation state prediction still remains elusive so far, which is more important in new material discovery for which the structures are not even available. This work proposes a novel deep learning based BERT transformer language model BERTOS for predicting the oxidation states of all elements of inorganic compounds given only their chemical composition. Our model achieves 96.82\% accuracy for all-element oxidation states prediction benchmarked on the cleaned ICSD dataset and achieves 97.61\% accuracy for oxide materials. We also demonstrate how it can be used to conduct large-scale screening of hypothetical material compositions for materials discovery., Comment: 16 pages

Uncertainty quantification (UQ) has increasing importance in building robust high-performance and generalizable materials property prediction models. It can also be used in active learning to train better models by focusing on getting new training data from uncertain regions. There are several categories of UQ methods each considering different types of uncertainty sources. Here we conduct a comprehensive evaluation on the UQ methods for graph neural network based materials property prediction and evaluate how they truly reflect the uncertainty that we want in error bound estimation or active learning. Our experimental results over four crystal materials datasets (including formation energy, adsorption energy, total energy, and band gap properties) show that the popular ensemble methods for uncertainty estimation is NOT the best choice for UQ in materials property prediction. For the convenience of the community, all the source code and data sets can be accessed freely at \url{https://github.com/usccolumbia/materialsUQ}.

Self-supervised neural language models have recently found wide applications in 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 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 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, Comment: 13 pages

Protein structures and functions are determined by a contiguous arrangement of amino acid sequences. Designing novel protein sequences and structures with desired geometry and functions is a complex task with large state spaces. Here we develop a novel protein design pipeline consisting of two deep learning algorithms, ProteinSolver and AlphaFold2. ProteinSolver is a deep graph neural network that generates amino acid sequences such that the forces between interacting amino acids are favorable and compatible with the fold while AlphaFold2 is a deep learning algorithm that predicts the protein structures from protein sequences. We present forty de novo designed binding sites of the PTP1B and P53 proteins with high precision, out of which thirty proteins are novel. Using ProteinSolver and AlphaFold2 in conjunction, we can trim the exploration of the large protein conformation space, thus expanding the ability to find novel and diverse de novo protein designs., Comment: 17 pages

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., Comment: 18 pages

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}., Comment: 18 pages

Efficient and accurate interatomic potential functions are critical to computational study of materials while searching for structures with desired properties. Traditionally, potential functions or energy landscapes are designed by experts based on theoretical or heuristic knowledge. Here, we propose a new approach to leverage strongly typed parallel genetic programming (GP) for potential function discovery. We use a multi-objective evolutionary algorithm with NSGA-III selection to optimize individual age, fitness, and complexity through symbolic regression. With a DFT dataset of 863 unique carbon allotrope configurations drawn from 858 carbon structures, the generated potentials are able to predict total energies within $\pm 7.70$ eV at low computational cost while generalizing well across multiple carbon structures. Our code is open source and available at \url{http://www.github.com/usccolumbia/mlpotential, Comment: 17 pages

Discovering new materials is a challenging task in materials science crucial to the progress of human society. Conventional approaches based on experiments and simulations are labor-intensive or costly with success heavily depending on experts' heuristic knowledge. Here, we propose a deep learning based Physics Guided Crystal Generative Model (PGCGM) for efficient crystal material design with high structural diversity and symmetry. Our model increases the generation validity by more than 700\% compared to FTCP, one of the latest structure generators and by more than 45\% compared to our previous CubicGAN model. Density Functional Theory (DFT) calculations are used to validate the generated structures with 1,869 materials out of 2,000 are successfully optimized and deposited into the Carolina Materials Database \url{www.carolinamatdb.org}, of which 39.6\% have negative formation energy and 5.3\% have energy-above-hull less than 0.25 eV/atom, indicating their thermodynamic stability and potential synthesizability., Comment: 18 pages, 5 figures, 7 tables

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 predictions. Benchmark studies on two datasets 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 new materials discovery., Comment: 17 pages

Data driven generative machine learning models have recently emerged as one of the most promising approaches for new materials discovery. While the generator models can generate millions of candidates, it is critical to train fast and accurate machine learning models to filter out stable, synthesizable materials with desired properties. However, such efforts to build supervised regression or classification screening models have been severely hindered by the lack of unstable or unsynthesizable samples, which usually are not collected and deposited in materials databases such as ICSD and Materials Project (MP). At the same time, there are a significant amount of unlabelled data available in these databases. Here we propose a semi-supervised deep neural network (TSDNN) model for high-performance formation energy and synthesizability prediction, which is achieved via its unique teacher-student dual network architecture and its effective exploitation of the large amount of unlabeled data. For formation energy based stability screening, our semi-supervised classifier achieves an absolute 10.3\% accuracy improvement compared to the baseline CGCNN regression model. For synthesizability prediction, our model significantly increases the baseline PU learning's true positive rate from 87.9\% to 97.9\% using 1/49 model parameters. To further prove the effectiveness of our models, we combined our TSDNN-energy and TSDNN-synthesizability models with our CubicGAN generator to discover novel stable cubic structures. Out of 1000 recommended candidate samples by our models, 512 of them have negative formation energies as validated by our DFT formation energy calculations. Our experimental results show that our semi-supervised deep neural networks can significantly improve the screening accuracy in large-scale generative materials design., Comment: 18 pages

Deep learning based generative models such as deepfake have been able to generate amazing images and videos. However, these models may need significant transformation when applied to generate crystal materials structures in which the building blocks, the physical atoms are very different from the pixels. Naively transferred generative models tend to generate a large portion of physically infeasible crystal structures that are not stable or synthesizable. Herein we show that by exploiting and adding physically oriented data augmentation, loss function terms, and post processing, our deep adversarial network (GAN) based generative models can now generate crystal structures with higher physical feasibility and expand our previous models which can only create cubic structures.

Fast and accurate crystal structure prediction (CSP) algorithms and web servers are highly desirable for exploring and discovering new materials out of the infinite design space. However, currently, the computationally expensive first principle calculation based crystal structure prediction algorithms are applicable to relatively small systems and are out of reach of most materials researchers due to the requirement of high computing resources or the software cost related to ab initio code such as VASP. Several computational teams have used an element substitution approach for generating or predicting new structures, but usually in an ad hoc way. Here we develop a template based crystal structure prediction algorithm (TCSP) and its companion web server, which makes this tool to be accessible to all materials researchers. Our algorithm uses elemental/chemical similarity and oxidation states to guide the selection of template structures and then rank them based on the substitution compatibility and can return multiple predictions with ranking scores in a few minutes. Benchmark study on the ~98,290 formulas of the Materials Project database using leave-one-out evaluation shows that our algorithm can achieve high accuracy (for 13,145 target structures, TCSP predicted their structures with RMSD < 0.1) for a large portion of the formulas. We have also used TCSP to discover new materials of the Ga-B-N system showing its potential for high-throughput materials discovery. Our user-friendly web app TCSP can be accessed freely at \url{www.materialsatlas.org/crystalstructure} on our MaterialsAtlas.org web app platform., Comment: 14 pages

Lattice vibration frequencies are related to many important materials properties such as thermal and electrical conductivity as well as superconductivity. However, computational calculation of vibration frequencies using density functional theory (DFT) methods is too computationally demanding for a large number of samples in materials screening. Here we propose a deep graph neural network-based algorithm for predicting crystal vibration frequencies from crystal structures with high accuracy. Our algorithm addresses the variable dimension of vibration frequency spectrum using the zero padding scheme. Benchmark studies on two data sets with 15,000 and 35,552 samples show that the aggregated $R^2$ scores of the prediction reaches 0.554 and 0.724 respectively. Our work demonstrates the capability of deep graph neural networks to learn to predict phonon spectrum properties of crystal structures in addition to phonon density of states (DOS) and electronic DOS in which the output dimension is constant., Comment: 9 pages