Neural operator Res-FNO based on dual-view feature fusion and Fourier transform

Abstract

In recent years, neural operators have shown great advantages in solving partial differential equations by learning mappings between function spaces. In this paper, we propose a novel neural operator network to further improve the efficiency of operator learning from parameter space to solution space. We introduce Dual-view block in the architecture, which can better extract and fuse potential features under different visual fields. In addition, we also introduce the homeomorphic mapping and parameterized integration kernels directly in Fourier space, which is beneficial to capturing the specific frequency information required during function iteration. The test results on the standard benchmark (Representative Partial Differential Equations Benchmark) demonstrate that our neural operator not only has better accuracy than the baseline but also has a huge advantage in inference speed. In summary, we provide a new option for using data-driven machine learning methods to solve partial differential equations quickly, robustly, and accurately.