Machine Learning Enhances Bulk Modulus Prediction in High Entropy Alloys

In a paper published in the journal Scientific Reports, researchers showcased the utilization of machine learning (ML) models for predicting the bulk modulus in High Entropy Alloys (HEA). It marked the pioneering use of ML in optimizing HEA compositions to achieve superior bulk modulus values. They trained 12 ML algorithms to classify elemental compositions as HEA or non-HEA.

Study: Machine Learning Enhances Bulk Modulus Prediction in High Entropy Alloys. Image credit: GVLR/Shutterstock
Study: Machine Learning Enhances Bulk Modulus Prediction in High Entropy Alloys. Image credit: GVLR/Shutterstock

Among these models, the Gradient Boosting Classifier (GBC) emerged as the most accurate, while the LASSO Regression model delivered outstanding results for forecasting the bulk modulus of HEAs. This research effectively addresses the gap in HEA discovery and property analysis. By expediting material discovery through the creation of virtual alloy compositions with desirable bulk modulus for specific applications, this study paves the way for novel HEA applications.


HEAs, commonly known as high-entropy alloys, embody a new class of materials characterized by their intricate multi-component, equiatomic compositions, and high configurational entropy, showcasing distinct phase formations and exceptional properties. These alloys show immense potential for aerospace and high-pressure machinery applications due to their outstanding characteristics, particularly their bulk modulus (k), which critically determines compressibility and strength under extreme pressure.

Understanding the intricate relationship between elemental composition and bulk modulus is pivotal in swiftly discovering and designing HEAs tailored to specific mechanical traits. Despite significant advancements in ML-driven research focusing on HEA phase prediction and automated property estimation, optimizing compositions for higher bulk moduli remains a relatively uncharted frontier, emphasizing a substantial gap in this domain.

ML-Powered HEA Bulk Modulus Forecasting

The research approach centers on ML models to forecast the elemental composition yielding high bulk modulus (k) values in HEAs. The process commences with thorough data pre-processing, extracting raw alloy constituent data, and establishing correlations with HEA formation. This initial stage highlights a specific subgroup of 37 elements known for their recurrent presence in HEAs, forming the basis for correlating elemental compositions with distinct phases observed in these alloys.

The team implemented a user interface that guides the algorithm, enabling users to select elements and specify the desired phase for the investigated HEA. Subsequent stages include the generation of a composition matrix, HEA classification, and utilizing ML models to predict bulk modulus values. The algorithm operates in five stages, initially receiving user-input elements and desired phases. It constructs a composition matrix to explore potential alloy compositions using the chosen elements.

The HEA classifier then takes this matrix to categorize compositions into HEAs or non-HEAs. HEA compositions identified by the classifier proceed to the bulk modulus (BM) regression stage, which predicts bulk modulus values. The ultimate output encompasses the elemental composition that yields the highest bulk modulus and the corresponding identified HEAs.

The researchers thoroughly analyze HEA classification models, evaluating 12 ML algorithms. Among these, they prioritize recall as a crucial metric for performance comparison. The GBC emerges with the second-highest recall value of 0.71. Extensive optimization efforts are directed towards the GBC model, achieving an accuracy of 0.98 over the training set and 0.77 over the testing set. However, despite earning a recall of 0.73 on the test dataset, the GBC model misclassifies approximately 27% of HEAs as non-HEAs, potentially affecting the inclusion of valuable HEAs in subsequent prediction processes.

In the BM regressor stage, seven regression models are assessed, with the Lasso Regression demonstrating superior accuracy in predicting bulk modulus values. Its efficacy stems from its ability to manage high sparsity within the dataset and perform effective feature selection. Through rigorous validation and optimization, the Lasso Regression model attains a high level of accuracy in predicting bulk modulus values for HEAs, validated against experimental values reported in literature sources.

The methodologies employed encompass comprehensive pre-processing, ML classification, regression techniques, and extensive model optimization. Collectively, these strategies aim to forecast and pinpoint high-performing HEAs based on bulk modulus values, laying a robust foundation for expediting the discovery and design of HEAs exhibiting desirable mechanical properties.


To summarize, ML models like the GBC classifier and LASSO Regressor exhibit significant potential in identifying HEAs with optimal bulk modulus values. These predictions aid in selecting HEAs associated with the highest bulk modulus, particularly for high-strength applications. It effectively streamlines the search process for experimentalists striving to create HEAs with superior bulk moduli.

Moreover, this study's scope extends to exploring correlations between other properties of HEAs based on their elemental composition. The application of ML-based virtual HEA design diminishes reliance on traditional experimental methods, offering an efficient alternative. As datasets expand, there is a promising avenue for enhancing the accuracy of these models manifold. This progression could revolutionize materials science by leveraging data-driven methodologies for HEA development.

Journal reference:
Silpaja Chandrasekar

Written by

Silpaja Chandrasekar

Dr. Silpaja Chandrasekar has a Ph.D. in Computer Science from Anna University, Chennai. Her research expertise lies in analyzing traffic parameters under challenging environmental conditions. Additionally, she has gained valuable exposure to diverse research areas, such as detection, tracking, classification, medical image analysis, cancer cell detection, chemistry, and Hamiltonian walks.


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