Lattice Thermal Conductivity Prediction Using Symbolic Regression and Machine Learning.

Area of Science:

• Materials Science
• Computational Physics
• Chemical Engineering

Background:

• Accurate prediction of lattice thermal conductivity (κ_L) is crucial for designing advanced materials like thermoelectrics and thermal barrier coatings.
• Existing models, such as Debye-Callaway and Slack, often lack the required accuracy for inorganic compounds.
• Predicting κ_L is challenging due to complex material properties and interatomic interactions.

Purpose of the Study:

• To develop novel analytical models for lattice thermal conductivity (κ_L) using genetic programming-based symbolic regression (SR).
• To compare the performance of SR-derived models against established methods and machine learning algorithms.
• To assess the generalizability and limitations of predictive models, particularly in extrapolation scenarios.

Main Methods:

• Symbolic regression (SR) using genetic programming to discover analytical formulas for κ_L.
• Comparison with multilayer perceptron neural networks and random forest regression models.
• Hybrid cross-validation (CV) including K-fold CV and holdout validation for robust performance evaluation.

Main Results:

• Four novel analytical formulas for κ_L were discovered via SR, demonstrating superior performance compared to the Slack model on the evaluated dataset.
• The generated formulas were found to correctly represent the underlying physical laws governing lattice thermal conductivity.
• Both SR and machine learning models exhibited significant challenges in extrapolative predictions on datasets with distributions different from the training set.

Conclusions:

• Genetic programming-based symbolic regression offers a powerful approach for discovering accurate analytical models for lattice thermal conductivity.
• The developed SR models provide improved predictive capabilities over traditional methods for κ_L.
• Extrapolation remains a critical limitation for current predictive models, highlighting the need for further research in model generalizability.