Symbolic Regression for Materials Science: A Case Study for Lattice Thermal Conductivity

Artificial intelligence (AI) frameworks that are capable of creating reliable and interpretable models are paramount for discovering new functional materials. Here we present the  SISSO++ code [2], a new implementation of the sure independence screening and sparsifying operator (SISSO) approach [1]. As a combination of compressed sensing and symbolic regression, SISSO can deterministically find the optimal analytic expression for a property, to a user-defined level of complexity. SISSO++ provides both a high performance library to perform SISSO calculations and a user-friendly python interface that facilitate interfacing SISSO into existing frameworks. SISSO++ also includes updates to the SISSO methodology itself, e.g. non-linear parameterization of features and using multiple residuals for each iteration, by quantitatively developing an analytical representation of the thermal conductivity.  In particular, we discuss the link between a material's anharmonicity [3] and its thermal conductivity and demonstrate how the developed formalism accelerates rational materials design and discovery by orders of magnitude.

[1] R. Ouyang et al. Phys. Rev. Mat. 2. 083802 (2018)

[2] T. A. R. Purcell et al. submitted to J. Open Source. Softw.

[3] F. Knoop et al. Phys. Rev. Mat. 4. 083809 (2020)