Distilling physical origins of hardness in multi-principal element alloys directly from ensemble neural network models

Despite a plethora of data being generated on the mechanical behavior of multi-principal element alloys, a systematic assessment remains inaccessible via Edisonian approaches. We approach this challenge by considering the specific case of alloy hardness, and present a machine-learning framework that captures the essential physical features contributing to hardness and allows high-throughput exploration of multi-dimensional compositional space. The model, tested on diverse datasets, was used to explore and successfully predict hardness in AlxTiy(CrFeNi)1-x-y, HfxCoy(CrFeNi)1-x-y and Alx(TiZrHf)1-x systems supported by data from density-functional theory predicted phase stability and ordering behavior. The experimental validation of hardness was done on TiZrHfAlx. The selected systems pose diverse challenges due to the presence of ordering and clustering pairs, as well as vacancy-stabilized novel structures. We also present a detailed model analysis that integrates local partial-dependencies with a compositional-stimulus and model-response study to derive material-specific insights from the decision-making process.