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Prediction models of lattice thermal conductivity have wide applications inthe discovery of thermoelectrics, thermal barrier coatings, and thermalmanagement of semiconductors. kL is notoriously difficult to predict. Whileclassic models such as the Debye-Callaway model and the Slack model have beenused to approximate the kL of inorganic compounds, their accuracy is far frombeing satisfactory. Herein, we propose a genetic programming based SymbolicRegression approach for explicit kL models and compare it with Multi-LayerPerceptron neural networks and a Random Forest Regressor using a hybridcross-validation approach including both K-Fold CV and holdout validation. Fourformulae have been discovered by our symbolic regression approach thatoutperform the Slack formula as evaluated on our dataset. Through the analysisof our models' performance and the formulae generated, we found that thetrained formulae successfully reproduce the correct physical law that governsthe lattice thermal conductivity of materials. We also identified thatextrapolation prediction remains to be a key issue in both symbolic regressionand regular machine learning methods and find the distribution of the samplesplace a key role in training a prediction model with high generalizationcapability.

Lattice Thermal Conductivity Prediction using Symbolic Regression and Machine Learning