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.

With the growing computing power of high-performance computers, efficient parallel algorithms are becoming increasingly important in the development of Computational Fluid Dynamics(CFD). This research presents a novel parallel strategy based on asynchronous and package communication. This strategy tries to enhance the performance of large-scale computation for realistic complex geometry. The new strategy aggregates all communications and only requires communication once at each iteration step. Convergence of the new strategy is also proved and validated. Three numerical experiments demonstrates the exceptional parallel performance of the novel strategy in simulating complex geometry. When the number of CPU cores approach 26 thousand, strong scale parallel efficiency still remains at 74% based on 10.5 billion mesh elements. With 179,200 CPU cores and 10 billion mesh elements, weak scale parallel efficiency maintains at 90%. This research demonstrates that large-scale parallel computation can be applied efficiently in numerical simulation of a complex aircraft.

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