Weak Adversarial Networks for Solving Incompressible Navier-Stokes equations
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Organizer(s): |
Name:
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Affiliation:
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Country:
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Wenran Li
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School of Mathematics, Statistics and Mechanics, Beijing University of Technology
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Peoples Rep of China
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Rong Yang
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School of Mathematics, Statistics and Mechanics, Beijing University of Technology
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Peoples Rep of China
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Xin-Guang Yang
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Department of Mathematics and Information Science, Henan Normal University
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Peoples Rep of China
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Introduction:
| | Weak adversarial network (WAN) has been used to search the weak solution of many PDEs. For the incompressible Nevier-Stokes (NS) equations, there are two problems with the algorithm : 1. The stream function can only be used to solve the 2D incompressible Navier-Stokes equation problem, 2. the error of the stream function output by the network is small, however it leads to increased errors by obtaining the velocity function through automatic differentiation. Therefore, in the same test case, the errors of the velocities obtained by WAN often exceed the errors of the stream function by an order of magnitude. To deal with these two problems, we propose a new algorithm, where the network output directly provides the components of velocity without the need of computing the stream function. This method have 3 advantages: 1. It shows more accurate results without the process from stream function to velocity; 2. It can also solve high-dimensional NS equations; 3. It is much easier to do error analysis for this method. |
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