Uncovering the Relationship Between Thermal Conductivity and Anharmonicity with Symbolic Regression*

Quantitatively understanding the link between anharmonicity and thermal conductivity, κ, is pivotal to the search for better thermal insulators. While it is qualitatively known that more anharmonic materials have a lower κ, until recently, no quantitative measure of anharmonicity existed. Here we present descriptors of κ based on our new measure of anharmonicity, σ^A [1]. We find the analytical expressions with symbolic regression, via the sure-independence screening and sparsifying operator (SISSO) method [2]. To better capture the nonlinearities in the correlation between κ and σ^A, we introduce an automatic scaling and shifting of the input data when generating new features like exp(α x + a). Using our new strategy, we generate expressions that are competitive with those previously reported in the literature using only a third of primary the features [3], and reduce the models test error by a third when compared to traditional SISSO. Finally, we discuss the implications of the new models on future materials design.

[1] F. Knoop et al.; Phys. Rev. Mat. 4. 083809 (2020)
[2] R. Ouyang et al.; Phys. Rev. Mat. 2. 083802 (2018)
[3] L. Chen et al.; J. Com. Mat. Sci. 170. 109155 (2019)