REGULAR ARTICLE Sparse mixed linear modeling with anchor-based guidance for high-entropy alloy discovery Ryo Murakami a, Seiji Miura b, Akihiro Endo a and Satoshi Minamoto a a Materials Data Platform, Research Network and Facility Services Division, National Institute for Materials Science, Tsukuba 305-0044, Ibaraki, Japan b Division of Materials Science and Engineering, Faculty of Engineering, Hokkaido University, Sapporo 060-8628, Hokkaido, Japan ARTICLE HISTORY Compiled April 30, 2025 ABSTRACT High-entropy alloys have attracted attention for their exceptional mechanical properties and thermal stability. To solve this problem, machine learning techniques have been increasingly employed for property prediction and high-throughput screening. Nevertheless, highly accurate nonlinear models often suffer from a lack of interpretability, which is a major limitation. In this study, we focus on local data structures that emerge from the greedy search behavior inherent to experimental data acquisition. By introducing a linear and low-dimensional mixture regression model, we strike a balance between predictive performance and model interpretability. In addition, we develop an algorithm that simultaneously performs prediction and feature selection by considering multiple candidate descriptors. Through a case study on high-entropy alloys, this study introduces a method that combines anchor-guided clustering and sparse linear modeling to address biased data structures arising from greedy exploration in materials science. KEYWORDS Sparse modeling; Mixed linear model; Bayesian inference; Materials informatics; Data-driven science; High-entropy alloys 1. Introduction In recent years, high-entropy alloys (HEAs) have garnered attention as next-generation materials for their outstanding mechanical properties, thermal stability, and corrosion resistance [1,2]. Unlike conventional alloy designs, HEAs--also referred to as multi-principal element alloys--comprise multiple (typically five or more) principal elements, offering a high degree of chemical and structural freedom. This unique composition enables the exploration of novel properties unattainable in traditional materials systems.

Machine learning (ML) methods have drawn significant interest in material design and discovery. Graph neural networks (GNNs), in particular, have demonstrated strong potential for predicting material properties. The present study proposes a graph-based representation for modeling medium-entropy alloys (MEAs). Hybrid Monte-Carlo molecular dynamics (MC/MD) simulations are employed to achieve thermally stable structures across various annealing temperatures in an MEA. These simulations generate dump files and potential energy labels, which are used to construct graph representations of the atomic configurations. Edges are created between each atom and its 12 nearest neighbors without incorporating explicit edge features. These graphs then serve as input for a Graph Convolutional Neural Network (GCNN) based ML model to predict the system's potential energy. The GCNN architecture effectively captures the local environment and chemical ordering within the MEA structure. The GCNN-based ML model demonstrates strong performance in predicting potential energy at different steps, showing satisfactory results on both the training data and unseen configurations. Our approach presents a graph-based modeling framework for MEAs and high-entropy alloys (HEAs), which effectively captures the local chemical order (LCO) within the alloy structure. This allows us to predict key material properties influenced by LCO in both MEAs and HEAs, providing deeper insights into how atomic-scale arrangements affect the properties of these alloys.

Inverse materials design has proven successful in accelerating novel material discovery. Many inverse materials design methods use unsupervised learning where a latent space is learned to offer a compact description of materials representations. A latent space learned this way is likely to be entangled, in terms of the target property and other properties of the materials. This makes the inverse design process ambiguous. Here, we present a semi-supervised learning approach based on a disentangled variational autoencoder to learn a probabilistic relationship between features, latent variables and target properties. This approach is data efficient because it combines all labelled and unlabelled data in a coherent manner, and it uses expert-informed prior distributions to improve model robustness even with limited labelled data. It is in essence interpretable, as the learnable target property is disentangled out of the other properties of the materials, and an extra layer of interpretability can be provided by a post-hoc analysis of the classification head of the model. We demonstrate this new approach on an experimental high-entropy alloy dataset with chemical compositions as input and single-phase formation as the single target property. While single property is used in this work, the disentangled model can be extended to customize for inverse design of materials with multiple target properties.

Graph neural networks (GNNs) have excelled in predictive modeling for both crystals and molecules, owing to the expressiveness of graph representations. High-entropy alloys (HEAs), however, lack chemical long-range order, limiting the applicability of current graph representations. To overcome this challenge, we propose a representation of HEAs as a collection of local environment (LE) graphs. Based on this representation, we introduce the LESets machine learning model, an accurate, interpretable GNN for HEA property prediction. We demonstrate the accuracy of LESets in modeling the mechanical properties of quaternary HEAs. Through analyses and interpretation, we further extract insights into the modeling and design of HEAs. In a broader sense, LESets extends the potential applicability of GNNs to disordered materials with combinatorial complexity formed by diverse constituents and their flexible configurations.

Developing new materials takes a lot of time, money and effort. Recently, a POSTECH research team has taken a step closer to creating new materials by applying AI to develop high-entropy alloys (HEAs) which are coined as "alloy of alloys." A joint research team led by Professor Seungchul Lee, Ph.D. candidate Soo Young Lee, Professor Hyungyu Jin and Ph.D. candidate Seokyeong Byeon of the Department of Mechanical Engineering along with Professor Hyoung Seop Kim of the Department of Materials Science and Engineering have together developed a technique for phase prediction of HEAs using AI. The findings from the study were published in the latest issue of Materials and Design, an international journal on materials science. Metal materials are conventionally made by mixing the principal element for the desired property with two or three auxiliary elements.