Machine Learning-based estimation and explainable artificial intelligence-supported interpretation of the critical temperature from magnetic <i>ab initio</i> Heusler alloys data

Machine learning (ML) has impacted numerous areas of materials science, most prominently improving molecular simulations, where force fields were trained on previously relaxed structures. One natural next step is to predict material properties beyond structure. In this work, we investigate the applicability and explainability of ML methods in the use case of estimating the critical temperature <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:mo>(</a:mo><a:msub><a:mi>T</a:mi><a:mtext>c</a:mtext></a:msub><a:mo>)</a:mo></a:math> for magnetic Heusler alloys calculated using methods determined materials-specific magnetic interactions and a subsequent Monte Carlo (MC) approach. We compare the performance of regression and classification models to predict the range of the <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"><b:msub><b:mi>T</b:mi><b:mtext>c</b:mtext></b:msub></b:math> of given compounds without performing the MC calculations. Since the MC calculation requires computational resources in the same order of magnitude as the density functional theory (DFT) calculation, it would be advantageous to replace either step with a less computationally intensive method such as ML. We discuss the necessity to generate the magnetic results to make a quantitative prediction of the <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"><c:msub><c:mi>T</c:mi><c:mtext>c</c:mtext></c:msub></c:math>. We used state-of-the-art explainable artificial intelligence (XAI) methods to extract physical relations and deepen our understanding of patterns learned by our models from the examined data.