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)