Transfer learning for deep neural network-based partial differential equations solving

Abstract

Deep neural networks (DNNs) have recently shown great potential in solving partial differential equations (PDEs). The success of neural network-based surrogate models is attributed to their ability to learn a rich set of solution-related features. However, learning DNNs usually involves tedious training iterations to converge and requires a very large number of training data, which hinders the application of these models to complex physical contexts. To address this problem, we propose to apply the transfer learning approach to DNN-based PDE solving tasks. In our work, we create pairs of transfer experiments on Helmholtz and Navier-Stokes equations by constructing subtasks with different source terms and Reynolds numbers. We also conduct a series of experiments to investigate the degree of generality of the features between different equations. Our results demonstrate that despite differences in underlying PDE systems, the transfer methodology can lead to a significant improvement in the accuracy of the predicted solutions and achieve a maximum performance boost of 97.3% on widely used surrogate models.