Lattice Thermal Conductivity Prediction using Symbolic Regression and Machine Learning

TL;DR

This paper introduces a genetic programming-based symbolic regression method to predict lattice thermal conductivity, outperforming traditional models and neural networks, while highlighting challenges in extrapolation and data distribution.

Contribution

The study develops explicit formulae for kL prediction using symbolic regression, demonstrating improved accuracy over classic models and neural networks.

Findings

Four formulae outperform Slack model

Symbolic regression captures physical laws governing kL

Extrapolation remains a key challenge

Abstract

Prediction models of lattice thermal conductivity have wide applications in the discovery of thermoelectrics, thermal barrier coatings, and thermal management of semiconductors. kL is notoriously difficult to predict. While classic models such as the Debye-Callaway model and the Slack model have been used to approximate the kL of inorganic compounds, their accuracy is far from being satisfactory. Herein, we propose a genetic programming based Symbolic Regression approach for explicit kL models and compare it with Multi-Layer Perceptron neural networks and a Random Forest Regressor using a hybrid cross-validation approach including both K-Fold CV and holdout validation. Four formulae have been discovered by our symbolic regression 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 identified that extrapolation prediction remains to be a key issue in both symbolic regression and regular machine learning methods and find the distribution of the samples place a key role in training a prediction model with high generalization capability.