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Abstract Recent advancements in machine learning (ML) have revolutionized the field of high-performance materials design. However, developing robust ML models to decipher intricate structure-property relationships in materials remains challenging, primarily due to the limited availability of labeled datasets with well-characterized crystal structures. This is particularly pronounced in materials where functional properties are closely intertwined with their crystallographic symmetry. We introduce a self-supervised probabilistic model (SSPM) that autonomously learns unbiased atomic representations and the likelihood of compounds with given crystal structures, utilizing solely the existing crystal structure data from materials databases. SSPM significantly enhances the performance of downstream ML models by efficient atomic representations and accurately captures the probabilistic relationships between composition and crystal structure. We showcase SSPM’s capability by discovering shape memory alloys (SMAs). Amongst the top 50 predictions, 23 have been confirmed as SMAs either experimentally or theoretically, and a previously unknown SMA candidate, MgAu, has been identified.

Abstract Machine learning has been widely used to guide the search for new materials by learning the patterns underlying available data. However, the pure prediction-oriented search is often biased to interpolation due to the limited data in a large unexplored space. Here we present a sampling framework towards extrapolation, that integrates unsupervised clustering, interpretable analysis, and similarity evaluation to sample target candidates with improved properties from a vast search space. Using the design of superalloys with improved $${\gamma }^{{\prime} }$$ γ ′ -phase solvus temperature ( $${T}_{{\gamma }^{{\prime} }}$$ T γ ′ ) as a model case, we start with sparse data, and by a few experiments, we find nine new superalloys with chemistries distinct to those in the training data. Three of them show improved $${T}_{{\gamma }^{{\prime} }}$$ T γ ′ by about 50 °C, a large enhancement for superalloys. Moreover, we find two features characterizing mismatch in atomic size and mixing enthalpy linearly effect. This work demonstrates the capability of unsupervised learning to search for new materials when limited data is available.

Abstract Finding high temperature superconductors (HTS) has been a continuing challenge due to the difficulty in predicting the transition temperature (Tc) of superconductors. Recently, the efficiency of predicting Tc has been greatly improved via machine learning (ML). Unfortunately, prevailing ML models have not shown adequate generalization ability to find new HTS, yet. In this work, a graph neural network model is trained to predict the maximal Tc (Tcmax) of various materials. Our model reveals a close connection between Tcmax and chemical bonds. It suggests that shorter bond lengths are favored by high Tc, which is in coherence with previous domain knowledge. More importantly, it also indicates that chemical bonds consisting of some specific chemical elements are responsible for high Tc, which is new even to the human experts. It can provide a convenient guidance to the materials scientists in search of HTS.

Abstract Alloy synthesis and processing determine the design of alloys with desired microstructure and properties. However, using data science to identify optimal synthesis-design routes from a specified set of starting materials has been limited by large-scale data acquisition. Text mining has made it possible to convert scientific text into structured data collections. Still, the complexity, diversity, and flexibility of synthesis and processing expressions, and the lack of annotated corpora with a gold standard severely hinder accurate and efficient extraction. Here we introduce a semi-supervised text mining method to extract the parameters corresponding to the sequence of actions of synthesis and processing. We automatically extract a total of 9853 superalloy synthesis and processing actions with chemical compositions from a corpus of 16,604 superalloy articles published up to 2022. These have then been used to capture an explicitly expressed synthesis factor for predicting γ′ phase coarsening. The synthesis factor derived from text mining significantly improves the performance of the data-driven γ′ size prediction model. The method thus complements the use of data-driven approaches in the search for relationships between synthesis and structures.

In material science and engineering, obtaining a spectrum from a measurement is often time-consuming and its accurate prediction using data mining can also be difficult. In this work, we propose a machine learning strategy based on a deep neural network model to accurately predict the dielectric temperature spectrum for a typical multi-component ferroelectric system, i.e., (Ba1−x−yCaxSry)(Ti1−u−v−wZruSnvHfw)O3. The deep neural network model uses physical features as inputs and directly outputs the full spectrum, in addition to yielding the octahedral factor, Matyonov–Batsanov electronegativity, ratio of valence electron to nuclear charge, and core electron distance (Schubert) as four key descriptors. Owing to the physically meaningful features, our model exhibits better performance and generalization ability in the broader composition space of BaTiO3-based solid solutions. And the prediction accuracy is superior to traditional machine learning models that predict dielectric permittivity values at each temperature. Furthermore, the transition temperature and the degree of dispersion of the ferroelectric phase transition are easily extracted from the predicted spectra to provide richer physical information. The prediction is also experimentally validated by typical samples of (Ba0.85Ca0.15)(Ti0.98–xZrxHf0.02)O3. This work provides insights for accelerating spectra predictions and extracting ferroelectric phase transition information.

The determination of ductile-to-brittle transition temperatures (DBTT) in intermetallic compounds is crucial for assessing their practical applications. In this study, we investigate the intrinsic factors influencing the DBTT of Fe–Al intermetallic compounds through feature engineering. We developed and evaluated two machine learning strategies for this task. Comparing the strategy that incorporates all features, including alloy compositions and atomic features, with the strategy utilizing selected features, it is found that the latter demonstrates superior computational efficiency and reduces overfitting. Specifically, surrogate models based on two selected features, namely cohesive energy and ionization energy, enable accurate prediction of the DBTT of Fe–Al intermetallics, achieving an accuracy of 95%. Additionally, through symbolic regression, we derived a functional expression that captures the relationship between variations in the DBTT and the selected features of intermetallic compounds. These findings have the potential to serve as a valuable guide for optimizing intermetallic compounds.

Abstract Optimizing several properties simultaneously based on small data-driven machine learning in complex black-box scenarios can present difficulties and challenges. Here we employ a triple-objective optimization algorithm deduced from probability density functions of multivariate Gaussian distributions to optimize the γ′ volume fraction, size, and morphology in CoNiAlCr-based superalloys. The effectiveness of the algorithm is demonstrated by synthesizing alloys with desired γ/γ′ microstructure and optimizing γ′ microstructural parameters. In addition, the method leads to incorporating refractory elements to improve γ/γ′ microstructure in superalloys. After four iterations of experiments guided by the algorithm, we synthesize sixteen alloys of relatively high creep strength from ~120,000 candidates of which three possess high γ′ volume fraction (>54%), small γ′ size (77%).

Abstract Optimizing more than one property is inevitable in designing new materials; however, some properties are usually improved at the expense of others. Multi‐objective optimization methods in engineering and computer science have proven to be an effective means to optimize several different properties simultaneously. Here, we reviewed these approaches including scalarization, evolutionary algorithms, and especially Bayesian optimization. Their promising applications to a number of materials problems are also discussed in the paper.

Abstract Data provides a foundation for machine learning, which has accelerated data-driven materials design. The scientific literature contains a large amount of high-quality, reliable data, and automatically extracting data from the literature continues to be a challenge. We propose a natural language processing pipeline to capture both chemical composition and property data that allows analysis and prediction of superalloys. Within 3 h, 2531 records with both composition and property are extracted from 14,425 articles, covering γ′ solvus temperature, density, solidus, and liquidus temperatures. A data-driven model for γ′ solvus temperature is built to predict unexplored Co-based superalloys with high γ′ solvus temperatures within a relative error of 0.81%. We test the predictions via synthesis and characterization of three alloys. A web-based toolkit as an online open-source platform is provided and expected to serve as the basis for a general method to search for targeted materials using data extracted from the literature.

Phase boundary engineering through chemical alloying and phase control is a traditional approach to enhancing piezoelectric properties. Here, the authors design a strategy in alkali niobate films, utilizing alkali vacancies without alloying to form nanopillars enclosed.

Abstract Herein, we demonstrate how to predict and experimentally validate phase diagrams for multi‐component systems from a high‐dimensional virtual space of all possible phase diagrams involving several elements based on small existing experimental data. The experimental data for bulk phases for known systems represents a sampling from this space, and screening the space allows multi‐component phase diagrams with given design criteria to be built. This approach uses machine learning methods to predict phase diagrams and Bayesian experimental design to minimize experiments for refinement and validation, all within an active learning loop. The approach is proven by predicting and synthesizing the ferroelectric ceramic system (1‐ω)(Ba0.61Ca0.28Sr0.11TiO3)‐ω(BaTi0.888Zr0.0616Sn0.0028Hf0.0476O3) with a relatively high transition temperature and triple point, as well as the NiTi‐based pseudo‐binary phase diagram (1‐ω)(Ti0.309Ni0.485Hf0.20Zr0.006)‐ω(Ti0.309Ni0.485Hf0.07Zr0.068Nb0.068) designed for high transition temperature (ω ⩽ 1). Each phase diagram is validated and optimized through only three new experiments. The complexity of these compounds is beyond the reach of today's computational methods.

Experimental search for high-temperature ferroelectric perovskites is challenging due to the vast chemical space and lack of predictive guidelines. Here the authors demonstrate a two-step machine learning approach to sequentially guide experiments in search of promising perovskites with high ferroelectric Curie temperature.

Computational design of functional materials with broken inversion symmetry is a complex task. Here, the authors demonstrate an approach that integrates symmetry analysis, data science methods, and density functional theory to accelerate the selection and identification process in complex oxides.

Abstract The problem that is considered is that of maximizing the energy storage density of Pb‐free BaTiO3‐based dielectrics at low electric fields. It is demonstrated that how varying the size of the combinatorial search space influences the efficiency of material discovery by comparing the performance of two machine learning based approaches where different levels of physical insights are involved. It is started with physics intuition to provide guiding principles to find better performers lying in the crossover region in the composition–temperature phase diagram between the ferroelectric phase and relaxor ferroelectric phase. Such an approach is limiting for multidopant solid solutions and motivates the use of two data‐driven machine learning and design strategies with a feedback loop to experiments. Strategy I considers learning and property prediction on all the compounds, and strategy II learns to preselect compounds in the crossover region on which prediction is carried out. By performing only two active learning loops via strategy II, the compound (Ba0.86Ca0.14)(Ti0.79Zr0.11Hf0.10)O3 is synthesized with the largest energy storage density ≈73 mJ cm−3 at a field of 20 kV cm−1, and an insight into the relative performance of the strategies using varying levels of knowledge is provided.

Abstract Room‐temperature magnetoelectric (ME) coupling is developed in artificial multilayers and nanocomposites composed of magnetostrictive and electrostrictive materials. While the coupling mechanisms and strengths in multilayers are widely studied, they are largely unexplored in vertically aligned nanocomposites (VANs), even though theory has predicted that VANs exhibit much larger ME coupling coefficients than multilayer structures. Here, strong transverse and longitudinal ME coupling in epitaxial BaTiO3:CoFe2O4 VANs measured by both optical second harmonic generation and piezoresponse force microscopy under magnetic fields is reported. Phase field simulations have shown that the ME coupling strength strongly depends on the vertical interfacial area which is ultimately controlled by pillar size. The ME coupling in VANs is determined by the competition between the vertical interface coupling effect and the bulk volume conservation effect. The revealed mechanisms shed light on the physical insights of vertical interface coupling in VANs in general, which can be applied to a variety of nanocomposites with different functionalities beyond the studied ME coupling effect.

Design of materials with targeted properties requires innovative approaches to guide researchers through complex search space. Here, the authors report an adaptive design strategy, using inference and global optimization methods, which can find shape memory alloys with very low thermal hysteresis.

A key element of materials discovery and design is to learn from available data and prior knowledge to guide the next experiments or calculations in order to focus in on materials with targeted properties. We suggest that the tight coupling and feedback between experiments, theory and informatics demands a codesign approach, very reminiscent of computational codesign involving software and hardware in computer science. This requires dealing with a constrained optimization problem in which uncertainties are used to adaptively explore and exploit the predictions of a surrogate model to search the vast high dimensional space where the desired material may be found.