Lattice Thermal Conductivity Prediction Using Symbolic Regression and Machine Learning.

Prediction models of lattice thermal conductivity (κ) have wide applications in the discovery of thermoelectrics, thermal barrier coatings, and thermal management of semiconductors. However, κ is notoriously difficult to predict. Although classic models such as the Debye-Callaway model and the Slack model have been used to approximate the κ of inorganic compounds, their accuracy is far from being satisfactory. Herein we propose a genetic programming-based symbolic regression (SR) approach for finding analytical κ models and compare them with multilayer perceptron neural networks and random forest regression models using a hybrid cross-validation (CV) approach including both -fold CV and holdout validation. Four formulae have been discovered by our SR approach that outperform the Slack formula as evaluated on our dataset. Through the analysis of our models' performance and the formulae generated, we found that the trained formulae successfully reproduce the correct physical law that governs the lattice thermal conductivity of materials. We also systematically show that currently extrapolative prediction over datasets with different distributions as the training set remains to be a big challenge for both SR and machine learning-based prediction models.