Coupled partial differential equations (PDEs) are key tasks in modeling the complex
dynamics of many physical processes. Recently, neural operators have shown the
ability to solve PDEs by learning the integral kernel directly in Fourier/Wavelet
space, so the difficulty for solving the coupled PDEs depends on dealing with the
coupled mappings between the functions. Towards this end, we propose a coupled
multiwavelets neural operator (CMWNO) learning scheme by decoupling the
coupled integral kernels during the multiwavelet decomposition and reconstruction
procedures in the Wavelet space. The proposed model achieves significantly higher
accuracy compared to previous learning-based solvers in solving the coupled PDEs
including Gray-Scott (GS) equations and the non-local mean field game (MFG)
problem. According to our experimental results, the proposed model exhibits a
2ˆ „ 4ˆ improvement relative L2 error compared to the best results from the
state-of-the-art models.
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