In this paper, we develop a method for finding models of heat conduction via machine learning. Integrating machine learning and the conservation-dissipation formulism (CDF) of irreversible thermodynamics, we obtain a system of PDEs for the heat conduction. The learned PDEs satisfy the conservation-dissipation principle and thereby are hyperbolic balance laws, which can be solved by conventional numerical methods. In the training process, we use a "warm-up" technique and train a neural network by another trained neural network. Numerical tests show that the learned models can achieve very high accuracy, perform well in a long time for a wide range of Knudsen numbers, and have an excellent generalization ability.
- train
cd train
python train_GM_Kn_Step4.py # for G and M
python trainf_Kn.py # for F
- predict
cd predict
python PredictionU_Kn.py
- data
- training data: data_all0428
- predicting data: data_all0428S, data_all0428T2
- parameters of the well-trained networks: folders in predict
Jin Zhao, Weifeng Zhao, Zhiting Ma, Wen-An Yong, and Bin Dong. Finding Models of Heat Conduction via Machine Learning. Submitted and Under Review (IJHMT).