PHYSICS-INFORMED FOURIER NEURAL OPERATORS: A MACHINE LEARNING METHOD FOR PARAMETRIC PARTIAL DIFFERENTIAL EQUATIONS

Current methods achieved reasonable success in solving short-term parametric partial differential equations (PDEs). However, solving long-term PDEs remains challenging, and existing techniques also suffer from low efficiency due to requiring finely-resolved datasets. In this paper, we propose a physics- informed Fourier neural operator (PIFNO) for parametric PDEs, which incorporates physical knowledge through regularization. The numerical PDE problem is reformulated into an unconstrained optimization task, which we solve by using an enhanced architecture that facilitates longer-term datasets. We compare PIFNO against standard FNO on three benchmark PDEs. Results demonstrate improved long-term performance with PIFNO. Moreover, PIFNO only needs coarse dataset resolution, which enhances computational efficiency.