Kernel neural operator for efficient solving PDEs.

Recently, the development of neural networks for solving partial differential equations (PDEs) has been extended to neural operators, which directly learn the mapping from any functional parametric dependence to the solution. Thus, compared to classical numerical methods, neural operators demonstrate the advantage in solving a family of PDEs. Motivated by recently successful neural operator: Fourier neural operator (FNO), we design a novel neural operator based on the encoder-decoder frame- work and the general integral operator whose kernel function is represented by the kernel method. Comparing to FNO, the proposed model allows for an expressive and efficient architecture, which greatly reduces the number of parameters and also has desirable results on numerical experiments. [ABSTRACT FROM AUTHOR]