标题： 基于符号回归和机器学习的晶格热导率预测 显示英文标题

标题： Lattice Thermal Conductivity Prediction using Symbolic Regression and Machine Learning

摘要： 预测晶格热导率的模型在热电材料、热障涂层和半导体热管理的发现中有着广泛的应用。 kL 预测起来非常困难。 虽然经典的模型如德拜-卡拉万模型和斯拉克模型已被用来近似无机化合物的kL，但它们的准确性远不能令人满意。 在此，我们提出了一种基于遗传编程的符号回归方法来建立显式的kL模型，并使用包括K折交叉验证和保留验证的混合交叉验证方法将其与多层感知器神经网络和随机森林回归器进行比较。 通过我们的符号回归方法发现了四个公式，在我们的数据集上评估结果优于斯拉克公式。 通过对模型性能和生成公式的分析，我们发现训练后的公式成功地再现了控制材料晶格热导率的正确物理定律。 我们还发现，外推预测仍然是符号回归和常规机器学习方法中的一个关键问题，并且样本的分布在训练具有高泛化能力的预测模型中起着关键作用。 显示英文摘要

摘要： 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.