Machine Learning Framework Drives Search for Better Refractory High-Entropy Alloys

In an article recently published in the open-access journal npj Computational Materials, researchers discussed the intelligent framework based on machine learning (ML) for finding refractory high-entropy alloys with enhanced high-temperature yield strength.

Study: Machine-learning-based intelligent framework for discovering refractory high-entropy alloys with improved high-temperature yield strength. Image Credit: Quardia/


Promising materials known as high-entropy alloys (HEAs) have attracted a lot of interest. Refractory high-temperature alloys (RHEAs) have been demonstrated through experimental research to have better high-temperature strength than superalloys, making them a desirable class of alloys for further investigation for prospective usage in high-efficiency gas turbine engines.

HEAs provide enormous possibilities, but they also present difficult problems to the material scientists faced with examining a design space with an enormous number of potential compositions. The absence of a broad understanding of the variables that determine the chemical and mechanical characteristics of these complex alloy systems is one of the main challenges impeding the rapid development of HEA.

Modern high-resolution imaging techniques can be used to collect atomic and microstructural information, but because they are money- and time-consuming, they cannot fully investigate and characterize the enormous composition space. As a result, the main focus of HEA research has been on formulating guidelines for phase formation as well as atomic and microstructural characteristics.

The literature has extensive reports of work to categorize phases using criteria. However, creating standards for enhancing mechanical qualities is a subject that has received relatively little research. Recently, several publications have been published that use different ML techniques to forecast the stages of HEA.

About the Study

In this study, the authors discussed the construction of a cutting-edge machine learning system paired with optimization techniques to intelligently explore the huge compositional space and enhance high-temperature yield strengths.

The proposed yield strength model significantly outperformed the state-of-the-art method in terms of predicted accuracy, and it also offered inherent uncertainty quantification through the use of repeated k-fold cross-validation. The linked framework was utilized to identify RHEAs with higher high-temperature yield strength after creating and validating a reliable yield strength prediction model. RHEA compositions with maximal yield strength at a particular temperature were designed.

The team intended to replace the experiment-only cycle with intelligent ML-based models to filter HEAs and reduce the search space. As an illustration, this study examined the yield strengths of RHEAs and developed a thorough forward ML model by selecting important descriptors from a set of numerous descriptors. To find RHEA compositions with improved yield strengths, the forward model was combined with a stochastic genetic algorithm37.

Concerning determining factors enhancing yield strength at both low and high temperatures, significant insights were achieved.

The researchers analyzed to comprehend how the physical and thermodynamic characteristics contributed to the increased yield strength. RHEA compositions with yield strengths tailored for particular temperatures were identified using the proposed ML-based model.


Compared to the experimental data, the proposed model had a mean absolute error of 147 MPa for NbTaTiV and 224 MPa for CrMoNbV. The improved alloy outperformed the base alloy by 90 MPa at 25 °C. The yield strength of the 1000 °C optimum alloy showed a very different temperature dependence, remaining roughly constant between 25 and 800 °C. The basic alloy yield strength was increased by 13% at 1000 °C. However, the 1000 °C ideal alloy had a much lower yield strength at 25 °C. Significant improvements were made over the base alloy compositions at both 25 °C and 1000 °C.

The concentrations of Ti, Nb, and Zr were reduced relative to the base alloy for the 25 °C ideal alloys in almost comparable amounts. However, the concentrations of Mo and V were both dramatically raised. The Ti fraction was raised, and the V fraction remained almost unaltered for the 1000 °C ideal alloy.

The composition and descriptors of the alloys optimized for yield strength at 25 °C and 1000 °C differed noticeably, demonstrating that the mechanisms and standards for maximizing strength at low temperature and high temperature could differ significantly, and compositions that maximize yield strength at room temperature could not do so for high temperatures.


In conclusion, this study used ML and optimization to show how an intelligent computational framework could forecast RHEA yield strength and find RHEA compositions that theoretically outperform the initial RHEA. It was demonstrated that repeated k-fold cross-validation combined with feature selection is an efficient method for obtaining a more statistically significant prediction of all data points.

The authors combined the robust ML-based yield strength prediction model with a genetic algorithm to find RHEA compositions with enhanced yield strengths. The algorithm intelligently explored the complex composition space to maximum yield strength given a baseline beginning RHEA.

The idea was illustrated using three different base alloys from the RHEA literature. Optimal alloy compositions were predicted for both 25 °C and 1000 °C, with improved yield strengths as high as 80%. Using a broad strategy, the team projected the yield strengths at low and high temperatures for 252 equiatomic RHEA chemicals. Using the proposed generic approach, the elemental composition was tailored to the best candidate for each temperature.

The authors mentioned that the work presented in this study establishes a framework for tackling the enormous task of finding HEAs that experimentally satisfy requirements for numerous attributes.


Giles, S. A., Sengupta, D., Broderick, S. R., et al. Machine-learning-based intelligent framework for discovering refractory high-entropy alloys with improved high-temperature yield strength. npj Computational Materials 8, 235 (2022).

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Surbhi Jain

Written by

Surbhi Jain

Surbhi Jain is a freelance Technical writer based in Delhi, India. She holds a Ph.D. in Physics from the University of Delhi and has participated in several scientific, cultural, and sports events. Her academic background is in Material Science research with a specialization in the development of optical devices and sensors. She has extensive experience in content writing, editing, experimental data analysis, and project management and has published 7 research papers in Scopus-indexed journals and filed 2 Indian patents based on her research work. She is passionate about reading, writing, research, and technology, and enjoys cooking, acting, gardening, and sports.


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