The Inverse Heat Transfer Problem of Malan Loess Based on Machine Learning with Finite Element Solver as the Trainer

Abstract

This paper proposes an efficient neural network both in solving process and time for inverse problem of determining thermophysical parameters of Malan loess. In this work, a finite element method (FEM) model is built for the direct solution of dynamic heat transfer problem in Malan loess, which is used to create the samples for the inverse network. Even more, a horn-like network Parm-Net is established, which takes the nodal temperatures of samples as the input data and the thermophysical parameter as the output data. Besides, the hyperparameters of Parm-Net (the number of neurons, the number of hidden layers, learning rate and batch size) are discussed in detail. Finally, intensive numerical experiments are carried out to demonstrate the effectiveness of our inverse network. The results show that the errors of multiple thermophysical parameters are smaller than the input noise, illustrating that Parm-Net is effective and stable with respect to noisy data.