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.

One of the difficult requirements imposed on high-quality CFD mesh generation has been the ability to evaluate the mesh quality efficiently. Due to the lack of a general and effective evaluating criterion, the current mesh quality evaluation task mainly relies on various quality metrics for the shape of mesh elements, such as angle, radius, edge and contextual information collected by pre-processing software. However, this line of methods greatly increases the pre-processing cost and may not guarantee a precise quality result. In this paper, we provide a solution to solve the mentioned issues, resulting in a CNN model GridNet and the first mesh dataset NACA-Market. GridNet takes the mesh file as input and then automatically evaluates the mesh quality. Experiment results show that GridNet is capable of performing automatic mesh quality evaluation and outperforms the widely used classifiers. We hope that the proposed large benchmark collection and network could fill in the gaps in the fields of CNN-based mesh quality evaluation and provide potential future research directions in this field.