Symbolic Regression in Materials Science

One of the fundamental research objectives of materials science is to design new materials with optimal performance. Typical machine learning models could be powerful predictors but not ideal in terms of interpretability. Here we present on an alternative to machine-learning models: symbolic regression (SR), which simultaneously searches for the optimal form of a function and set of parameters to the given problem, and is a powerful regression technique when little if any a-priori knowledge of the data distribution is available. We present how SR can learn the Landau free energy expansion describing the structural phase transition in LaNiO₃ using existing computational data [1]. Our model is able to capture the coupling of the temperature and order parameter, and we successfully predicted the structural phase transition at high temperature. We encourage materials scientists to utilize SR to open challenges in materials research, which could potentially unearth hidden governing laws in materials science from a data-driven approach.

[1] Wang, Y.; Wagner, N.; Rondinelli, J. M. Symbolic Regression in Materials Science. MRS Communications 2019, 9 (3), 793–805.