Rare-earth permanent magnets are essential for renewable energy and electric vehicle technologies, but their dependence on critical rare-earth elements raises concerns regarding resource security, cost, and environmental impact. Here, we develop an integrated data-driven framework for the sustainable design of high-abundance rare-earth permanent magnets. A dataset containing 346 experimental samples was constructed to establish composition–property relationships for Br, Hcj, and (BH)max. Eight machine learning (ML) algorithms were compared, and the multi-layer perceptron (MLP) model exhibited the most balanced overall performance after model refinement. The optimized MLP achieved testing R2 values of 0.979, 0.901, and 0.955 for Br, Hcj, and (BH)max, respectively, and repeated five-fold cross-validation supported its robustness. SHapley Additive exPlanations analysis indicated that Nd exerted the strongest statistical influence on the predicted magnetic properties, while Ce and La also contributed through nonlinear composition-property associations. The optimized MLP model was subsequently integrated with non-dominated sorting genetic algorithm II and Technique for Order Preference by Similarity to Ideal Solution to balance predicted (BH)max, material cost, and a composition-related upstream global warming potential (GWP) indicator. The selected Ce-rich candidate achieved a predicted (BH)max of 35.16 MGOe, an estimated material cost of 4.78 $/kg, and a GWP indicator of 16.41 kg CO2-eq/kg. These results demonstrate the potential of interpretable ML combined with multi-objective optimization for screening resource-efficient permanent-magnet compositions.
Hardenability is a critical indicator for evaluating the mechanical performance and service reliability of gear steel. However, conventional Jominy end-quench testing is labor-intensive and time-consuming, and data sharing among different companies is often restricted, which further complicates hardenability assessment. To address these challenges, a federated learning–driven data fusion strategy incorporating a multi-regularized attention residual network model for hardenability prediction (MRAN-J9) is proposed. In this strategy, collaborative models are trained on heterogeneous data from multiple sources, improving predictive accuracy while preserving the privacy of each participant’s raw data. Additionally, stable predictive performance is evaluated on a completely independent external validation dataset containing 755 samples [the coefficient of determination (R2) = 0.88, root mean square error (RMSE) = 0.99, Rockwell hardness (HRC)], demonstrating the generalization capability and predictive stability. The results confirm the feasibility and effectiveness of federated learning for privacy-preserving multi-party collaborative modeling. Furthermore, integrating the MRAN-J9 model facilitates the effective exploitation of distributed multi-source data, providing a practical and reliable solution for hardenability prediction in complex industrial application scenarios.
High-entropy alloys (HEAs) exhibit exceptional stability in extreme environments, yet their expansive design space presents a “curse of dimensionality” for traditional discovery methods. While machine learning (ML) offers a data-driven paradigm for material screening, the scarcity of experimental data often results in overfitting and limited physical interpretability. To address these challenges, this study proposes a hybrid physics-informed machine learning (Hybrid PIML) framework for accelerated hardness prediction. By integrating classical solid solution strengthening theory with a residual learning artificial neural network (ANN), the model explicitly embeds the physical coupling of shear modulus and lattice distortion (G·δr2/3) as prior knowledge. This approach ensures predictions adhere to metallurgical principles while significantly outperforming benchmark algorithms, achieving a coefficient of determination (R2) of 0.976 and reducing the root mean square error (RMSE) by approximately 43%. SHapley Additive exPlanations (SHAP) analysis confirms that physics-enhanced features dominate the decision-making process, validating the model’s internalization of strengthening mechanisms. Furthermore, the research elucidates a phase-dependent non-linear correlation between hardness and yield strength, correcting the failure of the classical Tabor formula in work-hardening face-centered cubic (FCC) alloys. Finally, a high-throughput virtual screening funnel based on this framework successfully identified optimized non-equiatomic candidates within the refractory Co-Cr-Ti-Mo-W system. This work establishes a precise, physically consistent pathway for inverse material design under data-constrained conditions.
Sustainable hydrogen energy offers a promising solution to the growing global energy demand associated with fossil fuel consumption. The development of efficient electrocatalysts for the hydrogen evolution reaction (HER) is important, yet the high computational cost of density functional theory (DFT) limits the rapid screening of candidate materials. In this work, a machine learning-assisted framework integrated with DFT calculations is proposed to systematically investigate the HER performance of carbon nanotube (CNT)-supported single-atom catalysts (SACs). A dataset consisting of Gibbs free energy of hydrogen adsorption (Delta GH*) was constructed from DFT calculations, including 84 M-N4-CNT(n, n) models involving 28 transition-metal centers anchored on CNTs with three different chirality indices. Based on selected intrinsic transition-metal features and the CNT chirality index, a random forest regression (RFR) model was identified as the optimal model after comparison with multiple machine learning algorithms for predicting Delta GH*. The RFR model exhibited excellent predictive accuracy, achieving a coefficient of determination (R2) of 0.98 on the test set. Notably, when applied to previously unseen M-N4-CNT(7, 7) structures, the model maintained high reliability (R2 = 0.96), demonstrating stronggeneralization capability. Machine learning identified Fe-N4-CNT(7, 7) as a highly promising HER electrocatalyst, with further DFT-based kinetic analysis showing that it follows a Volmer-Tafel reaction pathway. In addition, the SISSO algorithm was employed to derive an interpretable descriptor for Delta GH* based on elemental properties, achieving high fitting accuracy across different chirality indices. This descriptor provides an efficient tool for rapid catalyst screening while offering mechanistic insights into the key factors governing HER activity in M-N4-CNT systems.
High-entropy alloys (HEAs) have attracted extensive attention due to their exceptional mechanical, physical, and chemical properties, making them promising candidates for extreme environments. Understanding the complex structure-property relationships in these multi-principal element systems is crucial for discovering and designing high-performance HEAs. However, their vast compositional space and high-dimensional chemical complexity pose major challenges to traditional trial-and-error design. Machine learning (ML) offers a transformative strategy to overcome these barriers by enabling data-driven exploration. This perspective first reviews the critical challenges currently limiting HEA development, then summarizes recent ML breakthroughs in phase formation prediction, multi-objective optimization, and accelerated atomistic simulations. Finally, we discuss ongoing challenges and propose future opportunities for integrating ML with experimental and computational methods to create more interpretable, data-efficient, and autonomous ML-driven HEA design frameworks.
