A Modified Sobolev-Norm Loss for Physics-Informed Seismic Wave Modeling

Full waveform inversion relies on accurate FD solvers but is computationally demanding. Recent surrogates like the Fourier Neural Operator (FNO) offer fast, flexible inference purely from data, while PINO adds physics via PDE residuals but requires careful selection of the PDE loss weight. This work enhances the Fourier Neural Operator by incorporating a Sobolev-norm physics-informed loss that penalizes deviations from the wave equation. Compared to a data-only loss, our physics-informed FNO has better physical consistence and enables direct, interpretable tuning of the loss weights.