A Statistical Learning Framework for Materials Science: Application to Elastic Moduli of k-nary Inorganic Polycrystalline Compounds

Computational Investigation of the Potential and Limitations of Machine Learning with Neural Network Circuits Based on Synaptic Transistors

Synaptic transistors have been proposed to implement neuron activation functions of neural networks (NNs). While promising to enable compact, fast, inexpensive, and energy-efficient dedicated NN circuits, they also have limitations compared to digital NNs (realized as codes for digital processors), including shape choices of the activation function using particular types of transistor implementation, and instabilities due to noise and other factors present in analog circuits. We present a computational study of the effects of these factors on NN performance and find that, while accuracy competitive with traditional NNs can be realized for many applications, there is high sensitivity to the instability in the shape of the activation function, suggesting that, when highly accurate NNs are required, high-precision circuitry should be developed beyond what has been reported for synaptic transistors to date.

Preparation of Thermochromic Vanadium Dioxide Films Assisted by Machine Learning

In recent years, smart windows have attracted widespread attention due to their ability to respond to external stimuli such as light, heat, and electricity, thereby intelligently adjusting the ultraviolet, visible, and near-infrared light in solar radiation. VO2(M) undergoes a reversible phase transition from an insulating phase (monoclinic, M) to a metallic phase (rutile, R) at a critical temperature of 68 °C, resulting in a significant difference in near-infrared transmittance, which is particularly suitable for use in energy-saving smart windows. However, due to the multiple valence states of vanadium ions and the multiphase characteristics of VO2, there are still challenges in preparing pure-phase VO2(M). Machine learning (ML) can learn and generate models capable of predicting unknown data from vast datasets, thereby avoiding the wastage of experimental resources and reducing time costs associated with material preparation optimization. Hence, in this paper, four ML algorithms, namely multi-layer perceptron (MLP), random forest (RF), support vector machine (SVM), and extreme gradient boosting (XGB), were employed to explore the parameters for the successful preparation of VO2(M) films via magnetron sputtering. A comprehensive performance evaluation was conducted on these four models. The results indicated that XGB was the top-performing model, achieving a prediction accuracy of up to 88.52%. A feature importance analysis using the SHAP method revealed that substrate temperature had an essential impact on the preparation of VO2(M). Furthermore, characteristic parameters such as sputtering power, substrate temperature, and substrate type were optimized to obtain pure-phase VO2(M) films. Finally, it was experimentally verified that VO2(M) films can be successfully prepared using optimized parameters. These findings suggest that ML-assisted material preparation is highly feasible, substantially reducing resource wastage resulting from experimental trial and error, thereby promoting research on material preparation optimization.

Discovering melting temperature prediction models of inorganic solids by combining supervised and unsupervised learning

The melting temperature is important for materials design because of its relationship with thermal stability, synthesis, and processing conditions. Current empirical and computational melting point estimation techniques are limited in scope, computational feasibility, or interpretability. We report the development of a machine learning methodology for predicting melting temperatures of binary ionic solid materials. We evaluated different machine-learning models trained on a dataset of the melting points of 476 non-metallic crystalline binary compounds using materials embeddings constructed from elemental properties and density-functional theory calculations as model inputs. A direct supervised-learning approach yields a mean absolute error of around 180 K but suffers from low interpretability. We find that the fidelity of predictions can further be improved by introducing an additional unsupervised-learning step that first classifies the materials before the melting-point regression. Not only does this two-step model exhibit improved accuracy, but the approach also provides a level of interpretability with insights into feature importance and different types of melting that depend on the specific atomic bonding inside a material. Motivated by this finding, we used a symbolic learning approach to find interpretable physical models for the melting temperature, which recovered the best-performing features from both prior models and provided additional interpretability.

Informatics-Driven Design of Superhard B-C-O Compounds

Materials containing B, C, and O, due to the advantages of forming strong covalent bonds, may lead to materials that are superhard, i.e., those with a Vicker's hardness larger than 40 GPa. However, the exploration of this vast chemical, compositional, and configurational space is nontrivial. Here, we leverage a combination of machine learning (ML) and first-principles calculations to enable and accelerate such a targeted search. The ML models first screen for potentially superhard B-C-O compositions from a large hypothetical B-C-O candidate space. Atomic-level structure search using density functional theory (DFT) within those identified compositions, followed by further detailed analyses, unravels on four potentially superhard B-C-O phases exhibiting thermodynamic, mechanical, and dynamic stability.

Gradient boosted and statistical feature selection workflow for materials property predictions

With the emergence of big data initiatives and the wealth of available chemical data, data-driven approaches are becoming a vital component of materials discovery pipelines or workflows. The screening of materials using machine-learning models, in particular, is increasingly gaining momentum to accelerate the discovery of new materials. However, the black-box treatment of machine-learning methods suffers from a lack of model interpretability, as feature relevance and interactions can be overlooked or disregarded. In addition, naive approaches to model training often lead to irrelevant features being used which necessitates the need for various regularization techniques to achieve model generalization; this incurs a high computational cost. We present a feature-selection workflow that overcomes this problem by leveraging a gradient boosting framework and statistical feature analyses to identify a subset of features, in a recursive manner, which maximizes their relevance to the target variable or classes. We subsequently obtain minimal feature redundancy through multicollinearity reduction by performing feature correlation and hierarchical cluster analyses. The features are further refined using a wrapper method, which follows a greedy search approach by evaluating all possible feature combinations against the evaluation criterion. A case study on elastic material-property prediction and a case study on the classification of materials by their metallicity are used to illustrate the use of our proposed workflow; although it is highly general, as demonstrated through our wider subsequent prediction of various material properties. Our Bayesian-optimized machine-learning models generated results, without the use of regularization techniques, which are comparable to the state-of-the-art that are reported in the scientific literature.

Hybrid BO-XGBoost and BO-RF Models for the Strength Prediction of Self-Compacting Mortars with Parametric Analysis

Self-compacting mortar (SCM) has superior workability and long-term durable performance compared to traditional mortar. The strength of SCM, including both its compressive and flexural strengths, is a crucial property that is determined by appropriate curing conditions and mix design parameters. In the context of materials science, predicting the strength of SCM is challenging because of multiple influencing factors. This study employed machine learning techniques to establish SCM strength prediction models. Based on ten different input parameters, the strength of SCM specimens were predicted using two different types of hybrid machine learning (HML) models, namely Extreme Gradient Boosting (XGBoost) and the Random Forest (RF) algorithm. HML models were trained and tested by experimental data from 320 test specimens. In addition, the Bayesian optimization method was utilized to fine tune the hyperparameters of the employed algorithms, and cross-validation was employed to partition the database into multiple folds for a more thorough exploration of the hyperparameter space while providing a more accurate assessment of the model's predictive power. The results show that both HML models can successfully predict the SCM strength values with high accuracy, and the Bo-XGB model demonstrated higher accuracy (R² = 0.96 for training and R² = 0.91 for testing phases) for predicting flexural strength with low error. In terms of compressive strength prediction, the employed BO-RF model performed very well, with R² = 0.96 for train and R² = 0.88 testing stages with minor errors. Moreover, the SHAP algorithm, permutation importance and leave-one-out importance score were used for sensitivity analysis to explain the prediction process and interpret the governing input variable parameters of the proposed HML models. Finally, the outcomes of this study might be applied to guide the future mix design of SCM specimens.

Exploring the Possibility of Machine Learning for Predicting Ionic Conductivity of Solid-State Electrolytes

Unlike conventional liquid electrolytes, solid-state electrolytes (SSEs) have gained increased attention in the domain of all-solid-state lithium-ion batteries (ASSBs) due to their safety features, higher energy/power density, better electrochemical stability, and a broader electrochemical window. SSEs, however, face several difficulties, such as poorer ionic conductivity, complicated interfaces, and unstable physical characteristics. Vast research is still needed to find compatible and appropriate SSEs with improved properties for ASSBs. Traditional trial-and-error procedures to find novel and sophisticated SSEs require vast resources and time. Machine learning (ML), which has emerged as an effective and trustworthy tool for screening new functional materials, was recently used to forecast new SSEs for ASSBs. In this study, we developed an ML-based architecture to predict ionic conductivity by utilizing the characteristics of activation energy, operating temperature, lattice parameters, and unit cell volume of various SSEs. Additionally, the feature set can identify distinct patterns in the data set that can be verified using a correlation map. Because they are more reliable, the ensemble-based predictor models can more precisely forecast ionic conductivity. The prediction can be strengthened even further, and the overfitting issue can be resolved by stacking numerous ensemble models. The data set was split into 70:30 ratios to train and test with eight predictor models. The maximum mean-squared error and mean absolute error in training and testing for the random forest regressor (RFR) model were obtained as 0.001 and 0.003, respectively.

Need for UAI–Anatomy of the Paradigm of Usable Artificial Intelligence for Domain-Specific AI Applicability

Data-driven methods based on artificial intelligence (AI) are powerful yet flexible tools for gathering knowledge and automating complex tasks in many areas of science and practice. Despite the rapid development of the field, the existing potential of AI methods to solve recent industrial, corporate and social challenges has not yet been fully exploited. Research shows the insufficient practicality of AI in domain-specific contexts as one of the main application hurdles. Focusing on industrial demands, this publication introduces a new paradigm in terms of applicability of AI methods, called Usable AI (UAI). Aspects of easily accessible, domain-specific AI methods are derived, which address essential user-oriented AI services within the UAI paradigm: usability, suitability, integrability and interoperability. The relevance of UAI is clarified by describing challenges, hurdles and peculiarities of AI applications in the production area, whereby the following user roles have been abstracted: developers of cyber–physical production systems (CPPS), developers of processes and operators of processes. The analysis shows that target artifacts, motivation, knowledge horizon and challenges differ for the user roles. Therefore, UAI shall enable domain- and user-role-specific adaptation of affordances accompanied by adaptive support of vertical and horizontal integration across the domains and user roles.

Large Data Set-Driven Machine Learning Models for Accurate Prediction of the Thermoelectric Figure of Merit

The figure of merit (zT) is a key parameter to measure the performance of thermoelectric materials. At present, the prediction of zT values via machine leaning has emerged as a promising method for exploring high-performance materials. However, the machine learning-based predictions still suffer from unsatisfactory accuracy, and this is related to the size of the data set, the hyperparameters of models, and the quality of the data. In this work, 5038 pieces of data of thermoelectric materials were selected, and several regression models were generated to predict zT values. This large data set-driven light gradient boosting (LGB) model with 57 features performed with an excellent accuracy, achieving a coefficient of determination (R²) value of 0.959, a root mean squared error (RMSE) of 0.094, a mean absolute error (MAE) of 0.057, and a correlation coefficient (R) of 0.979. Owing to the large size of the data set, the prediction accuracy exceeds that of most reported zT predictions via machine learning. The "M_E Lattice Parameter" was verified as the most important feature in the zT prediction. Furthermore, nine potential candidates were screened out from among one million pieces of data. This study solves the problem of the data set size, adjusts the hyperparameters of the models, uses feature engineering to improve data quality, and provides an efficient strategy to perform wide-ranging screening for promising materials.

Materials Genomics Search for Possible Helium-Absorbing Nano-Phases in Fusion Structural Materials

Civilian fusion demands structural materials that can withstand the harsh environments imposed inside fusion plasma reactors. The structural materials often transmute under 14.1 MeV fast neutrons, producing helium (He), which embrittles the grain boundary (GB) network. Here, it is shown that neutron-friendly and mechanically strong nano-phases with atomic-scale free volume can have low He-embedding energy E emb ${\mathcal{E}}_{\mathrm{emb}}$ and >10 at.% He-absorbing capacity, and can be especially advantageous for soaking up He on top of resisting radiation damage and creep, provided they have thermodynamic compatibility with the matrix phase, satisfactory equilibrium wetting angle, as well as a high enough melting point. The preliminary experimental demonstration proves that E emb ${\mathcal{E}}_{\mathrm{emb}}$ is a good ab initio predictor of He shielding potency in nano-heterophase materials, and thus, E emb ${\mathcal{E}}_{\mathrm{emb}}$ is used as a key feature for computational screening. In this context, a list of viable compounds expected to be good He-absorbing nano-phases is presented, taking into account E emb ${\mathcal{E}}_{\mathrm{emb}}$ , the neutron absorption and activation cross-sections, the elastic moduli, melting temperature, the thermodynamic compatibility, and the equilbrium wetting angle of the nano-phases with the Fe matrix as an example.

Physics-Guided Descriptors for Prediction of Structural Polymorphs

We develop a method combining machine learning (ML) and density functional theory (DFT) to predict low-energy polymorphs by introducing physics-guided descriptors based on structural distortion modes. We systematically generate crystal structures utilizing the distortion modes and compute their energies with single-point DFT calculations. We then train a ML model to identify low-energy configurations on the material's high-dimensional potential energy surface. Here, we use BiFeO₃ as a case study and explore its phase space by tuning the amplitudes of linear combinations of a finite set of distinct distortion modes. Our procedure is validated by rediscovering several known metastable phases of BiFeO₃ with complex crystal structures, and its efficiency is proved by identifying 21 new low-energy polymorphs. This approach proposes a new avenue toward accelerating the prediction of low-energy polymorphs in solid-state materials.

Moving closer to experimental level materials property prediction using AI

While experiments and DFT-computations have been the primary means for understanding the chemical and physical properties of crystalline materials, experiments are expensive and DFT-computations are time-consuming and have significant discrepancies against experiments. Currently, predictive modeling based on DFT-computations have provided a rapid screening method for materials candidates for further DFT-computations and experiments; however, such models inherit the large discrepancies from the DFT-based training data. Here, we demonstrate how AI can be leveraged together with DFT to compute materials properties more accurately than DFT itself by focusing on the critical materials science task of predicting “formation energy of a material given its structure and composition”. On an experimental hold-out test set containing 137 entries, AI can predict formation energy from materials structure and composition with a mean absolute error (MAE) of 0.064 eV/atom; comparing this against DFT-computations, we find that AI can significantly outperform DFT computations for the same task (discrepancies of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$>0.076$$\end{document}>0.076 eV/atom) for the first time.

Accelerating amorphous polymer electrolyte screening by learning to reduce errors in molecular dynamics simulated properties

Polymer electrolytes are promising candidates for the next generation lithium-ion battery technology. Large scale screening of polymer electrolytes is hindered by the significant cost of molecular dynamics (MD) simulation in amorphous systems: the amorphous structure of polymers requires multiple, repeated sampling to reduce noise and the slow relaxation requires long simulation time for convergence. Here, we accelerate the screening with a multi-task graph neural network that learns from a large amount of noisy, unconverged, short MD data and a small number of converged, long MD data. We achieve accurate predictions of 4 different converged properties and screen a space of 6247 polymers that is orders of magnitude larger than previous computational studies. Further, we extract several design principles for polymer electrolytes and provide an open dataset for the community. Our approach could be applicable to a broad class of material discovery problems that involve the simulation of complex, amorphous materials.

Screening polymer electrolytes for batteries is extremely expensive due to the complex structures and slow dynamics. Here the authors develop a machine learning scheme to accelerate the screening and explore a space much larger than past studies.

Machine learning of material properties: Predictive and interpretable multilinear models

Machine learning models can provide fast and accurate predictions of material properties but often lack transparency. Interpretability techniques can be used with black box solutions, or alternatively, models can be created that are directly interpretable. We revisit material datasets used in several works and demonstrate that simple linear combinations of nonlinear basis functions can be created, which have comparable accuracy to the kernel and neural network approaches originally used. Linear solutions can accurately predict the bandgap and formation energy of transparent conducting oxides, the spin states for transition metal complexes, and the formation energy for elpasolite structures. We demonstrate how linear solutions can provide interpretable predictive models and highlight the new insights that can be found when a model can be directly understood from its coefficients and functional form. Furthermore, we discuss how to recognize when intrinsically interpretable solutions may be the best route to interpretability.

A compilation of experimental data on the mechanical properties and microstructural features of Ti-alloys

The present work depicts a compilation of mechanical properties of 282 distinct multicomponent Ti-based alloys and their respective microstructural features. The dataset includes the chemical composition (in at.%), phase constituents, Young modulus, hardness, yield strength, ultimate strength, and elongation. Each entry is associated with a high-quality experimental work containing a complete description of the processing route and testing setup. Furthermore, we incorporated flags to the dataset indicating (a) the use of high-resolution techniques for microstructural analysis and (b) the observation of non-linear elastic responses during mechanical testing. Oxygen content and average grain size are presented whenever available. The selected features can help material scientists to adjust the data to their needs concerning materials selection and discovery. Most alloys in the dataset were produced via an ingot metallurgy route, followed by solubilization and water quench (≈58%), which is considered a standard condition for β-Ti alloys. The database is hosted and maintained up to date in an open platform. For completeness, a few graphical representations of the dataset are included.

Measurement(s)	elastic modulus • mechanical strength (yield) • deformation at rupture • Vickers hardness • oxygen content • grain size • mechanical strength (ultimate)
Technology Type(s)	longitudinal and transversal pulse-echo ultrasound, nanoidentation, mechanical testing • mechanical testing (tensile), mechanical testing (compression) • Vickers hardness testing • inert gas fusion chemical analysis • linear intercept method
Sample Characteristic - Organism	metallic alloys
Sample Characteristic - Environment	room temperature

Environmental Stability of Crystals: A Greedy Screening

Discovering materials that are environmentally stable and also exhibit the necessary collection of properties required for a particular application is a perennial challenge in materials science. Herein, we present an algorithm to rapidly screen materials for their thermodynamic stability in a given environment, using a greedy approach. The performance was tested against the standard energy above the hull stability metric for inert conditions. Using data of 126 320 crystals, the greedy algorithm was shown to estimate the driving force for decomposition with a mean absolute error of 39.5 meV/atom, giving it sufficient resolution to identify stable materials. To demonstrate the utility outside of a vacuum, the in-oxygen stability of 39 654 materials was tested. The enthalpy of oxidation was found to be largely exothermic. Further analysis showed that 1438 of these materials fall into the range required for self-passivation based on the Pilling-Bedworth ratio.

Density of states prediction for materials discovery via contrastive learning from probabilistic embeddings

Machine learning for materials discovery has largely focused on predicting an individual scalar rather than multiple related properties, where spectral properties are an important example. Fundamental spectral properties include the phonon density of states (phDOS) and the electronic density of states (eDOS), which individually or collectively are the origins of a breadth of materials observables and functions. Building upon the success of graph attention networks for encoding crystalline materials, we introduce a probabilistic embedding generator specifically tailored to the prediction of spectral properties. Coupled with supervised contrastive learning, our materials-to-spectrum (Mat2Spec) model outperforms state-of-the-art methods for predicting ab initio phDOS and eDOS for crystalline materials. We demonstrate Mat2Spec's ability to identify eDOS gaps below the Fermi energy, validating predictions with ab initio calculations and thereby discovering candidate thermoelectrics and transparent conductors. Mat2Spec is an exemplar framework for predicting spectral properties of materials via strategically incorporated machine learning techniques.

Uncertainty Prediction for Machine Learning Models of Material Properties

Uncertainty quantification in artificial intelligence (AI)-based predictions of material properties is of immense importance for the success and reliability of AI applications in materials science. While confidence intervals are commonly reported for machine learning (ML) models, prediction intervals, i.e., the evaluation of the uncertainty on each prediction, are not as frequently available. In this work, we compare three different approaches to obtain such individual uncertainty, testing them on 12 ML-physical properties. Specifically, we investigated using the quantile loss function, machine learning the prediction intervals directly, and using Gaussian processes. We identify each approach's advantages and disadvantages and end up slightly favoring the modeling of the individual uncertainties directly, as it is the easiest to fit and, in most of the cases, minimizes over- and underestimation of the predicted errors. All data for training and testing were taken from the publicly available JARVIS-DFT database, and the codes developed for computing the prediction intervals are available through the JARVIS-tools package.

Superhydrophobic Polymer Topography Design Assisted by Machine Learning Algorithms

Superhydrophobic surfaces have been largely achieved through various surface topographies. Both empirical and numerical simulations have been reported to help understand and design superhydrophobic surfaces. Many such successful surfaces have also been achieved using bioinspired and biomimetic designs. Despite this, identifying the right surface texture to meet the requirements of specific applications is not a straightforward task. Here, we report a hybrid approach that includes experimental methods, numerical simulations, and machine learning (ML) algorithms to create design maps for superhydrophobic polymer topographies. Two design objectives to investigate superhydrophobic properties were the maximum water contact angle (WCA) and Laplace pressure. The design parameters were the geometries of an isotropic pillar structure in micrometer and sub-micrometer length scales. The finite element method (FEM) was validated by the experimental data and employed to generate a labeled dataset for ML training. Artificial neural network (ANN) models were then trained on the labeled database for the topographic parameters (width W, height H, and pitch P) with the corresponding WCA and Laplace pressure. The ANN models yielded a series of nonlinear relationships between the topographic design parameters and the WCA and Laplace pressure and substantial differences between the micrometer and sub-micrometer length scales. Design maps that span the topography design parameters provide optimal design or tradeoff parameters. This research demonstrates the potential of ANN as a rapid design tool for surface topography exploration.

Ensemble machine learning methods: predicting electron stopping powers from a small experimental database

Electron stopping power (SP) is of great importance in theoretical and applied research areas specifically for Monte Carlo simulation studies in many microanalysis and surface analysis techniques, radiation dosimetry, and the design of particle detectors. However, experimental data are available for a dozen elemental materials only. On the other hand, the Bethe analytical expression of the SP is applicable at high energies only whereas no generally accepted formula exists at lower energies. We employed ensemble machine learning (ML) methods with the available experimental database for the prediction of SPs of electrons with energies from 100 keV down to 1 eV, in elements over the entire periodic table. With a small training database for electron SPs, we applied various algorithms individually as well as their ensembles, which have the credibility to enhance the prediction accuracy in the case of a small training database. Based on the model's performance evaluation tests, we concluded that the stacked generalization is more accurate than the individual algorithms. Using this method, we were able to predict the electron SPs for 54 elements (in total) including 12 elements that were present in the training database as well as for 42 elements beyond the training database over a wide energy range (1 eV to 100 keV). Compared to other theoretical approaches, the ML predicted SPs show very good agreement with the available experimental data at all energies. Moreover, unlike other theoretical approaches, the ML model does not need dielectric function data and other physical parameters which involve complex calculations. Using our ML model, we have predicted SPs for a further 14 elements for which no theoretical SPs are available because of the lack of good dielectric function data.

Discovery of Low-Modulus Ti-Nb-Zr Alloys Based on Machine Learning and First-Principles Calculations

The discovery of low-modulus Ti alloys for biomedical applications is challenging due to a vast number of compositions and available solute contents. In this work, machine learning (ML) methods are employed for the prediction of the bulk modulus (K) and the shear modulus (G) of optimized ternary alloys. As a starting point, the elasticity data of more than 1800 compounds from the Materials Project fed linear models, random forest regressors, and artificial neural networks (NN), with the aims of training predictive models for K and G based on compositional features. The models were then used to predict the resultant Young modulus (E) for all possible compositions in the Ti-Nb-Zr system, with variations in the composition of 2 at. %. Random forest (RF) predictions of E deviate from the NN predictions by less than 4 GPa, which is within the expected variance from the ML training phase. RF regressors seem to generate the most reliable models, given the selected target variables and descriptors. Optimal compositions identified by the ML models were later investigated with the aid of special quasi-random structures (SQSs) and density functional theory (DFT). According to a combined analysis, alloys with 22 Zr (at. %) are promising structural materials to the biomedical field, given their low elastic modulus and elevated beta-phase stability. In alloys with Nb content higher than 14.8 (at. %), the beta phase has lower energy than omega, which may be enough to avoid the formation of omega, a high-modulus phase, during manufacturing.

Predictive Modeling of Critical Temperatures in Superconducting Materials

In this study, we have investigated quantitative relationships between critical temperatures of superconductive inorganic materials and the basic physicochemical attributes of these materials (also called quantitative structure-property relationships). We demonstrated that one of the most recent studies (titled "A data-driven statistical model for predicting the critical temperature of a superconductor” and published in Computational Materials Science by K. Hamidieh in 2018) reports on models that were based on the dataset that contains 27% of duplicate entries. We aimed to deliver stable models for a properly cleaned dataset using the same modeling techniques (multiple linear regression, MLR, and gradient boosting decision trees, XGBoost). The predictive ability of our best XGBoost model (R2 = 0.924, RMSE = 9.336 using 10-fold cross-validation) is comparable to the XGBoost model by the author of the initial dataset (R2 = 0.920 and RMSE = 9.5 K in ten-fold cross-validation). At the same time, our best model is based on less sophisticated parameters, which allows one to make more accurate interpretations while maintaining a generalizable model. In particular, we found that the highest relative influence is attributed to variables that represent the thermal conductivity of materials. In addition to MLR and XGBoost, we explored the potential of other machine learning techniques (NN, neural networks and RF, random forests).

Extending the Applicability of the ANI Deep Learning Molecular Potential to Sulfur and Halogens

Machine learning (ML) methods have become powerful, predictive tools in a wide range of applications, such as facial recognition and autonomous vehicles. In the sciences, computational chemists and physicists have been using ML for the prediction of physical phenomena, such as atomistic potential energy surfaces and reaction pathways. Transferable ML potentials, such as ANI-1x, have been developed with the goal of accurately simulating organic molecules containing the chemical elements H, C, N, and O. Here, we provide an extension of the ANI-1x model. The new model, dubbed ANI-2x, is trained to three additional chemical elements: S, F, and Cl. Additionally, ANI-2x underwent torsional refinement training to better predict molecular torsion profiles. These new features open a wide range of new applications within organic chemistry and drug development. These seven elements (H, C, N, O, F, Cl, and S) make up ∼90% of drug-like molecules. To show that these additions do not sacrifice accuracy, we have tested this model across a range of organic molecules and applications, including the COMP6 benchmark, dihedral rotations, conformer scoring, and nonbonded interactions. ANI-2x is shown to accurately predict molecular energies compared to density functional theory with a ∼10⁶ factor speedup and a negligible slowdown compared to ANI-1x and shows subchemical accuracy across most of the COMP6 benchmark. The resulting model is a valuable tool for drug development which can potentially replace both quantum calculations and classical force fields for a myriad of applications.

QSAR without borders

Prediction of chemical bioactivity and physical properties has been one of the most important applications of statistical and more recently, machine learning and artificial intelligence methods in chemical sciences. This field of research, broadly known as quantitative structure-activity relationships (QSAR) modeling, has developed many important algorithms and has found a broad range of applications in physical organic and medicinal chemistry in the past 55+ years. This Perspective summarizes recent technological advances in QSAR modeling but it also highlights the applicability of algorithms, modeling methods, and validation practices developed in QSAR to a wide range of research areas outside of traditional QSAR boundaries including synthesis planning, nanotechnology, materials science, biomaterials, and clinical informatics. As modern research methods generate rapidly increasing amounts of data, the knowledge of robust data-driven modelling methods professed within the QSAR field can become essential for scientists working both within and outside of chemical research. We hope that this contribution highlighting the generalizable components of QSAR modeling will serve to address this challenge.

Topology-Based Machine Learning Strategy for Cluster Structure Prediction

In cluster physics, the determination of the ground-state structure of medium-sized and large-sized clusters is a challenge due to the number of local minimal values on the potential energy surface growing exponentially with cluster size. Although machine learning approaches have had much success in materials sciences, their applications in clusters are often hindered by the geometric complexity clusters. Persistent homology provides a new topological strategy to simplify geometric complexity while retaining important chemical and physical information without having to "downgrade" the original data. We further propose persistent pairwise independence (PPI) to enhance the predictive power of persistent homology. We construct topology-based machine learning models to reveal hidden structure-energy relationships in lithium (Li) clusters. We integrate the topology-based machine learning models, a particle swarm optimization algorithm, and density functional theory calculations to accelerate the search of the globally stable structure of clusters.

Enhancing materials property prediction by leveraging computational and experimental data using deep transfer learning

The current predictive modeling techniques applied to Density Functional Theory (DFT) computations have helped accelerate the process of materials discovery by providing significantly faster methods to scan materials candidates, thereby reducing the search space for future DFT computations and experiments. However, in addition to prediction error against DFT-computed properties, such predictive models also inherit the DFT-computation discrepancies against experimentally measured properties. To address this challenge, we demonstrate that using deep transfer learning, existing large DFT-computational data sets (such as the Open Quantum Materials Database (OQMD)) can be leveraged together with other smaller DFT-computed data sets as well as available experimental observations to build robust prediction models. We build a highly accurate model for predicting formation energy of materials from their compositions; using an experimental data set of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$1,963$$\end{document}1,963 observations, the proposed approach yields a mean absolute error (MAE) of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$0.06$$\end{document}0.06 eV/atom, which is significantly better than existing machine learning (ML) prediction modeling based on DFT computations and is comparable to the MAE of DFT-computation itself.

Machine-learning approaches based on DFT computations can greatly enhance materials discovery. Here the authors leverage existing large DFT-computational data sets and experimental observations by deep transfer learning to predict the formation energy of materials from their elemental compositions with high accuracy.

Nanoinformatics, and the big challenges for the science of small things

The combination of computational chemistry and computational materials science with machine learning and artificial intelligence provides a powerful way of relating structural features of nanomaterials with functional properties. However, combining these fundamentally different scientific approaches is not as straightforward as it seems. Machine learning methods were developed for large data sets with small numbers of consistent features. Typically nanomaterials data sets are small, with high dimensionality and high variance in the feature space, and suffer from numerous destructive biases. None of the established data science or machine learning methods in widespread use today were devised with (nano)materials data sets in mind, but there are ways to overcome these challenges and use them reliably. In this review we will discuss domain-specific constraints on data-driven nanomaterials design, and explore the differences between nanomaterials simulation and nanoinformatics that can be leveraged for greater impact.

Local electronic descriptors for solute-defect interactions in bcc refractory metals

The interactions between solute atoms and crystalline defects such as vacancies, dislocations, and grain boundaries are essential in determining alloy properties. Here we present a general linear correlation between two descriptors of local electronic structures and the solute-defect interaction energies in binary alloys of body-centered-cubic (bcc) refractory metals (such as W and Ta) with transition-metal substitutional solutes. One electronic descriptor is the bimodality of the d-orbital local density of states for a matrix atom at the substitutional site, and the other is related to the hybridization strength between the valance sp- and d-bands for the same matrix atom. For a particular pair of solute-matrix elements, this linear correlation is valid independent of types of defects and the locations of substitutional sites. These results provide the possibility to apply local electronic descriptors for quantitative and efficient predictions on the solute-defect interactions and defect properties in alloys.

Modelling of framework materials at multiple scales: current practices and open questions

The last decade has seen an explosion of the family of framework materials and their study, from both the experimental and computational points of view. We propose here a short highlight of the current state of methodologies for modelling framework materials at multiple scales, putting together a brief review of new methods and recent endeavours in this area, as well as outlining some of the open challenges in this field. We will detail advances in atomistic simulation methods, the development of material databases and the growing use of machine learning for the prediction of properties. This article is part of the theme issue 'Mineralomimesis: natural and synthetic frameworks in science and technology'.

Discovering unusual structures from exception using big data and machine learning techniques

Recently, machine learning (ML) has become a widely used technique in materials science study. Most work focuses on predicting the rule and overall trend by building a machine learning model. However, new insights are often learnt from exceptions against the overall trend. In this work, we demonstrate that how unusual structures are discovered from exceptions when machine learning is used to get the relationship between atomic and electronic structures based on big data from high-throughput calculation database. For example, after training an ML model for the relationship between atomic and electronic structures of crystals, we find AgO₂F, an unusual structure with both Ag³⁺ and O₂^2-, from structures whose band gap deviates much from the prediction made by our model. A further investigation on this structure might shed light into the research on anionic redox in transition metal oxides of Li-ion batteries.

Materials Science in the AI age: high-throughput library generation, machine learning and a pathway from correlations to the underpinning physics

The use of advanced data analytics and applications of statistical and machine learning approaches ('AI') to materials science is experiencing explosive growth recently. In this prospective, we review recent work focusing on generation and application of libraries from both experiment and theoretical tools, across length scales. The available library data both enables classical correlative machine learning, and also opens the pathway for exploration of underlying causative physical behaviors. We highlight the key advances facilitated by this approach, and illustrate how modeling, macroscopic experiments and atomic-scale imaging can be combined to dramatically accelerate understanding and development of new material systems via a statistical physics framework. These developments point towards a data driven future wherein knowledge can be aggregated and used collectively, accelerating the advancement of materials science.

Accelerated Discovery of Efficient Solar-cell Materials using Quantum and Machine-learning Methods

Solar-energy plays an important role in solving serious environmental problems and meeting high-energy demand. However, the lack of suitable materials hinders further progress of this technology. Here, we present the largest inorganic solar-cell material search to date using density functional theory (DFT) and machine-learning approaches. We calculated the spectroscopic limited maximum efficiency (SLME) using Tran-Blaha modified Becke-Johnson potential for 5097 non-metallic materials and identified 1997 candidates with an SLME higher than 10%, including 934 candidates with suitable convex-hull stability and effective carrier mass. Screening for 2D-layered cases, we found 58 potential materials and performed G0W0 calculations on a subset to estimate the prediction-uncertainty. As the above DFT methods are still computationally expensive, we developed a high accuracy machine learning model to pre-screen efficient materials and applied it to over a million materials. Our results provide a general framework and universal strategy for the design of high-efficiency solar cell materials. The data and tools are publicly distributed at: https://www.ctcms.nist.gov/~knc6/JVASP.html, https://www.ctcms.nist.gov/jarvisml/, https://jarvis.nist.gov/ and https://github.com/usnistgov/jarvis.

ElemNet: Deep Learning the Chemistry of Materials From Only Elemental Composition

Conventional machine learning approaches for predicting material properties from elemental compositions have emphasized the importance of leveraging domain knowledge when designing model inputs. Here, we demonstrate that by using a deep learning approach, we can bypass such manual feature engineering requiring domain knowledge and achieve much better results, even with only a few thousand training samples. We present the design and implementation of a deep neural network model referred to as ElemNet; it automatically captures the physical and chemical interactions and similarities between different elements using artificial intelligence which allows it to predict the materials properties with better accuracy and speed. The speed and best-in-class accuracy of ElemNet enable us to perform a fast and robust screening for new material candidates in a huge combinatorial space; where we predict hundreds of thousands of chemical systems that could contain yet-undiscovered compounds.

Machine Learning Enabled Computational Screening of Inorganic Solid Electrolytes for Suppression of Dendrite Formation in Lithium Metal Anodes

Next generation batteries based on lithium (Li) metal anodes have been plagued by the dendritic electrodeposition of Li metal on the anode during cycling, resulting in short circuit and capacity loss. Suppression of dendritic growth through the use of solid electrolytes has emerged as one of the most promising strategies for enabling the use of Li metal anodes. We perform a computational screening of over 12 000 inorganic solids based on their ability to suppress dendrite initiation in contact with Li metal anode. Properties for mechanically isotropic and anisotropic interfaces that can be used in stability criteria for determining the propensity of dendrite initiation are usually obtained from computationally expensive first-principles methods. In order to obtain a large data set for screening, we use machine-learning models to predict the mechanical properties of several new solid electrolytes. The machine-learning models are trained on purely structural features of the material, which do not require any first-principles calculations. We train a graph convolutional neural network on the shear and bulk moduli because of the availability of a large training data set with low noise due to low uncertainty in their first-principles-calculated values. We use gradient boosting regressor and kernel ridge regression to train the elastic constants, where the choice of the model depends on the size of the training data and the noise that it can handle. The material stiffness is found to increase with an increase in mass density and ratio of Li and sublattice bond ionicity, and decrease with increase in volume per atom and sublattice electronegativity. Cross-validation/test performance suggests our models generalize well. We predict over 20 mechanically anisotropic interfaces between Li metal and four solid electrolytes which can be used to suppress dendrite growth. Our screened candidates are generally soft and highly anisotropic, and present opportunities for simultaneously obtaining dendrite suppression and high ionic conductivity in solid electrolytes.

Genarris: Random generation of molecular crystal structures and fast screening with a Harris approximation

We present Genarris, a Python package that performs configuration space screening for molecular crystals of rigid molecules by random sampling with physical constraints. For fast energy evaluations, Genarris employs a Harris approximation, whereby the total density of a molecular crystal is constructed via superposition of single molecule densities. Dispersion-inclusive density functional theory is then used for the Harris density without performing a self-consistency cycle. Genarris uses machine learning for clustering, based on a relative coordinate descriptor developed specifically for molecular crystals, which is shown to be robust in identifying packing motif similarity. In addition to random structure generation, Genarris offers three workflows based on different sequences of successive clustering and selection steps: the "Rigorous" workflow is an exhaustive exploration of the potential energy landscape, the "Energy" workflow produces a set of low energy structures, and the "Diverse" workflow produces a maximally diverse set of structures. The latter is recommended for generating initial populations for genetic algorithms. Here, the implementation of Genarris is reported and its application is demonstrated for three test cases.

Crystal Graph Convolutional Neural Networks for an Accurate and Interpretable Prediction of Material Properties

The use of machine learning methods for accelerating the design of crystalline materials usually requires manually constructed feature vectors or complex transformation of atom coordinates to input the crystal structure, which either constrains the model to certain crystal types or makes it difficult to provide chemical insights. Here, we develop a crystal graph convolutional neural networks framework to directly learn material properties from the connection of atoms in the crystal, providing a universal and interpretable representation of crystalline materials. Our method provides a highly accurate prediction of density functional theory calculated properties for eight different properties of crystals with various structure types and compositions after being trained with 10^{4} data points. Further, our framework is interpretable because one can extract the contributions from local chemical environments to global properties. Using an example of perovskites, we show how this information can be utilized to discover empirical rules for materials design.

Thermal expansion of quaternary nitride coatings

The thermal expansion coefficient of technologically relevant multicomponent cubic nitride alloys are predicted using the Debye model with ab initio elastic constants calculated at 0 K and an isotropic approximation for the Grüneisen parameter. Our method is benchmarked against measured thermal expansion of TiN and Ti_(1-x)Al _x N as well as against results of molecular dynamics simulations. We show that the thermal expansion coefficients of Ti_(1-x-y)X _y Al _x N (X  =  Zr, Hf, Nb, V, Ta) solid solutions monotonously increase with the amount of alloying element X at all temperatures except for Zr and Hf, for which they instead decrease for [Formula: see text].

A general representation scheme for crystalline solids based on Voronoi-tessellation real feature values and atomic property data

Increasing attention has been paid to materials informatics approaches that promise efficient and fast discovery and optimization of functional inorganic materials. Technical breakthrough is urgently requested to advance this field and efforts have been made in the development of materials descriptors to encode or represent characteristics of crystalline solids, such as chemical composition, crystal structure, electronic structure, etc. We propose a general representation scheme for crystalline solids that lifts restrictions on atom ordering, cell periodicity, and system cell size based on structural descriptors of directly binned Voronoi-tessellation real feature values and atomic/chemical descriptors based on the electronegativity of elements in the crystal. Comparison was made vs. radial distribution function (RDF) feature vector, in terms of predictive accuracy on density functional theory (DFT) material properties: cohesive energy (CE), density (d), electronic band gap (BG), and decomposition energy (Ed). It was confirmed that the proposed feature vector from Voronoi real value binning generally outperforms the RDF-based one for the prediction of aforementioned properties. Together with electronegativity-based features, Voronoi-tessellation features from a given crystal structure that are derived from second-nearest neighbor information contribute significantly towards prediction.

Machine learning for the structure-energy-property landscapes of molecular crystals

Molecular crystals play an important role in several fields of science and technology. They frequently crystallize in different polymorphs with substantially different physical properties. To help guide the synthesis of candidate materials, atomic-scale modelling can be used to enumerate the stable polymorphs and to predict their properties, as well as to propose heuristic rules to rationalize the correlations between crystal structure and materials properties. Here we show how a recently-developed machine-learning (ML) framework can be used to achieve inexpensive and accurate predictions of the stability and properties of polymorphs, and a data-driven classification that is less biased and more flexible than typical heuristic rules. We discuss, as examples, the lattice energy and property landscapes of pentacene and two azapentacene isomers that are of interest as organic semiconductor materials. We show that we can estimate force field or DFT lattice energies with sub-kJ mol-1 accuracy, using only a few hundred reference configurations, and reduce by a factor of ten the computational effort needed to predict charge mobility in the crystal structures. The automatic structural classification of the polymorphs reveals a more detailed picture of molecular packing than that provided by conventional heuristics, and helps disentangle the role of hydrogen bonded and π-stacking interactions in determining molecular self-assembly. This observation demonstrates that ML is not just a black-box scheme to interpolate between reference calculations, but can also be used as a tool to gain intuitive insights into structure-property relations in molecular crystal engineering.