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1. Insights on phase formation from thermodynamic calculations and machine learning of 2436 experimentally measured high entropy alloys

   https://doi.org/10.1016/j.jallcom.2022.165173  

   Wang, Chuangye; Zhong, Wei; Zhao, Ji-Cheng (September 2022, Journal of Alloys and Compounds)

   Both CALPHAD (CALculation of PHAse Diagrams) and machine-learning (ML) approaches were employed to analyze the phase formation in 2,436 experimentally measured high entropy alloy (HEA) compositions consisting of various quinary mixtures of Al, Co, Cr, Cu, Fe, Mn, and Ni. CALPHAD was found to have good capabilities in predicting the BCC/B2 and FCC phase formation for the 1,761 solid-solution-only compositions, excluding HEAs containing an amorphous phase (AM) or/and intermetallic compound (IM). Phase selection rules were examined systematically using several parameters and it revealed that valency electron concentration (VEC) < 6.87 and VEC > 9.16 are the conditions for the formation of single-phase BCC/B2 and FCC, respectively; and CALPHAD could predict this with essentially 100% accuracy. Both CALPHAD predictions and experimental observations show that more BCC/B2 alloys are formed over FCC alloys as the atomic size difference between the elements increases. Four machine learning (ML) algorithms, decision tree (DT), k-nearest neighbor (KNN), support vector machine (SVM), and artificial neural network (ANN), were employed to study the phase selection rules for two different datasets, one consisting of 1,761 solid-solution (SS) HEAs without AM and/or IM phases, and the other set consisting of all the 2,436 HEA compositions. Cross validation (CV) was performed to optimize the ML models and the CV accuracies are found to be 91.4%, 93.1%, 90.2%, 89.1% for DT, KNN, SVM, and ANN respectively in predicting the formation of BCC/B2, BCC/B2 + FCC, and FCC; and 93.6%, 93.3%, 95.5%, 92.7% for DT, KNN, SVM, and ANN respectively in predicting SS, AM, SS + AM, and IM phases. Sixty-six experimental bulk alloys with SS structures are predicted with trained ANN model, and the accuracy reaches 81.8%. VEC is found to be most important parameter in phase prediction for BCC/B2, BCC/B2 + FCC, and FCC phases. Electronegativity difference and FCC-BCC-index (FBI) are the two additional dominating features in determining the formation of SS, AM, SS + AM, and IM. A separation line ΔH_mix=28.97×VEC-246.77 was found in the VEC-vs-ΔH_mix plot to predict the formation of single-phase BCC/B2 or FCC with a 96.2% accuracy (ΔH_mix = mixing enthalpy). These insights will be very valuable for designing HEAs with targeted crystal structures. 

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2. Applications of machine learning in high-entropy alloys: a review of recent advances in design, discovery, and characterization

   https://doi.org/10.1039/D5NR01562F  

   Golbabaei, Mohammad Hossein; Zohrevand, Mohammad; Zhang, Ning (September 2025, Nanoscale)

   High-entropy alloys (HEAs) have attracted considerable attention due to their exceptional properties and outstanding performance across various applications. However, the vast compositional space and complex high-dimensional atomic interactions pose significant challenges in uncovering fundamental physical principles and effectively guiding alloy design. Traditional experimental approaches, often reliant on trial-and-error methods, are time-consuming, cost-prohibitive, and inefficient. To accelerate progress in this field, advanced simulation techniques and data-driven methodologies, particularly machine learning (ML) with a particular interest in nanoscale phenomena, have emerged as transformative tools for composition design, property prediction, and performance optimization. By leveraging extensive materials databases and sophisticated learning algorithms, ML facilitates the discovery of intricate patterns that conventional methods may overlook, and enables the design of HEAs with targeted properties. This review paper provides a comprehensive overview of recent advancements in ML applications for HEAs. It begins with a brief introduction of the fundamental principles of HEAs and ML methodologies, including key algorithms, databases, and evaluation metrics. The critical role of materials representation and feature engineering in ML-driven HEA design is thoroughly discussed. Furthermore, state-of-the-art developments in the integration of ML with HEA research, particularly in composition optimization, property prediction, and phase identification, are systematically reviewed. Special emphasis is placed on cutting-edge deep learning techniques, such as generative models and computer vision, which are revolutionizing the f ield. This study explores the application of machine learning (ML) in developing highly accurate ML interatomic potentials (MLIPs) for molecular dynamics (MD) simulations. These MLIPs have the potential to enhance the accuracy and efficiency of simulations, enabling a more precise representation of the fundamental physics governing high-entropy alloys (HEAs) at the atomic level. A critical discussion is provided, addressing both the potential advantages and the inherent limitations of this approach. This review aims to provide insights into the future directions of ML-driven HEA research, offering a roadmap for advancing material design through data-driven innovation. 

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3. Kolmogorov–Arnold neural networks for high-entropy alloys design

   https://doi.org/10.1088/1361-651X/adbb83  

   Bandyopadhyay, Yagnik; Avlani, Harshil; Zhuang, Houlong L (March 2025, Modelling and Simulation in Materials Science and Engineering)

   Abstract A wide range of deep learning-based machine learning (ML) techniques are extensively applied to the design of high-entropy alloys (HEAs), yielding numerous valuable insights. Kolmogorov–Arnold networks (KAN) is a recently developed architecture that aims to improve both the accuracy and interpretability of input features. In this work, we explore three different datasets for HEA design and demonstrate the application of KAN for both classification and regression models. In the first example, we use a KAN classification model to predict the probability of single-phase formation in high-entropy carbide ceramics based on various properties such as mixing enthalpy and valence electron concentration. In the second example, we employ a KAN regression model to predict the yield strength and ultimate tensile strength of HEAs based on their chemical composition and process conditions including annealing time, cold rolling percentage, and homogenization temperature. The third example involves a KAN classification model to determine whether a certain composition is an HEA or non-HEA, followed by a KAN regressor model to predict the bulk modulus of the identified HEA, aiming to identify HEAs with high bulk modulus. In all three examples, KAN either outperform or match the performance in terms of accuracy such asF1 score for classification and mean square error, and coefficient of determination (R²) for regression of the multilayer perceptron by demonstrating the efficacy of KAN in handling both classification and regression tasks. We provide a promising direction for future research to explore advanced ML techniques, which lead to more accurate predictions and better interpretability of complex materials, ultimately accelerating the discovery and optimization of HEAs with desirable properties. 

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4. Learning-Based Workload Phase Classification and Prediction Using Performance Monitoring Counters

   https://doi.org/10.1109/MLCAD52597.2021.9531161  

   Alcorta, Erika S.; Gerstlauer, Andreas (August 2021, ACM/IEEE Workshop on Machine Learning for CAD (MLCAD))

   null (Ed.)

   Predicting coarse-grain variations in workload behavior during execution is essential for dynamic resource optimization of processor systems. Researchers have proposed various methods to first classify workloads into phases and then learn their long-term phase behavior to predict and anticipate phase changes. Early studies on phase prediction proposed table-based phase predictors. More recently, simple learning-based techniques such as decision trees have been explored. However, more recent advances in machine learning have not been applied to phase prediction so far. Furthermore, existing phase predictors have been studied only in connection with specific phase classifiers even though there is a wide range of classification methods. Early work in phase classification proposed various clustering methods that required access to source code. Some later studies used performance monitoring counters, but they only evaluated classifiers for specific contexts such as thermal modeling. In this work, we perform a comprehensive study of source-oblivious phase classification and prediction methods using hardware counters. We adapt classification techniques that were used with different inputs in the past and compare them to state-of-the-art hardware counter based classifiers. We further evaluate the accuracy of various phase predictors when coupled with different phase classifiers and evaluate a range of advanced machine learning techniques, including SVMs and LSTMs for workload phase prediction. We apply classification and prediction approaches to SPEC workloads running on an Intel Core-i9 platform. Results show that a two-level kmeans clustering combined with SVM-based phase change prediction provides the best tradeoff between accuracy and long-term stability. Additionally, the SVM predictor reduces the average prediction error by 80% when compared to a table-based predictor. 

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5. A comparison of different machine learning algorithms for predicting student performance in an online interactive mathematics game.

   Lee, Ji-Eun; Jindal, Amisha; Patki, sanika Nitin; Gurung, Ashish; Norum, Reilly; Ottmar, Erin (May 2023, Interactive learning environments)

   This paper demonstrated how to apply Machine Learning (ML) techniques to analyze student interaction data collected in an online mathematics game. Using a data-driven approach, we examined 1) how different ML algorithms influenced the precision of middle-school students’ (N = 359) performance (i.e. posttest math knowledge scores) prediction and 2) what types of in-game features (i.e. student in-game behaviors, math anxiety, mathematical strategies) were associated with student math knowledge scores. The results indicated that the Random Forest algorithm showed the best performance (i.e. the accuracy of models, error measures) in predicting posttest math knowledge scores among the seven algorithms employed. Out of 37 features included in the model, the validity of the students’ first mathematical transformation was the most predictive of their posttest math knowledge scores. Implications for game learning analytics and supporting students’ algebraic learning are discussed based on the findings. 

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