  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 \textit{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 $2\times \sim 4\times$
improvement relative $L$2 error compared to the best results from the
state-of-the-art models.
