Discovering a formula for the high temperature oxidation behavior of FeCrAlCoNi based high entropy alloys by domain knowledge-guided machine learning

A mathematical formula of high physical interpretation, and accurate prediction and large generalization power is highly desirable for science, technology and engineering. In this study, we performed a domain knowledge-guided machine learning to discover high interpretive formula describing the high-temperature oxidation behavior of FeCrAlCoNi-based high entropy alloys (HEAs). The domain knowledge suggests that the exposure time dependent and thermally activated oxidation behavior can be described by the synergy formula of power law multiplying Arrhenius equation. The pre-factor, time exponent (m), and activation energy (Q) are dependent on the chemical compositions of eight elements in the FeCrAlCoNi-based HEAs. The Tree-Classifier for Linear Regression (TCLR) algorithm utilizes the two experimental features of exposure time (t) and temperature (T) to extract the spectrums of activation energy (Q) and time exponent (m) from the complex and high dimensional feature space, which automatically gives the spectrum of pre-factor. The three spectrums are assembled by using the element features, which leads to a general and interpretive formula with high prediction accuracy of the determination coefficient R2=0.971. The role of each chemical element in the high-temperature oxidation behavior is analytically illustrated in the three spectrums, thereby the discovered interpretative formula provides a guidance to the inverse design of HEAs against high-temperature oxidation. The present work demonstrates the significance of domain knowledge in the development of materials informatics.