Are Fourier Neural Operators Really Faster for Time-Domain Wave Propagation?

Abstract

Fourier Neural Operators (FNOs) have been promoted as fast, mesh-invariant surrogates for partial-differential equation solvers, with seismic studies reporting orders-of-magnitude speedup over classical methods. We revisit those claims by benchmarking a state-of-the-art Tucker-tensorized FNO (TFNO) against highly optimized, GPU-accelerated finite-difference (FD) codes for four wave-physics formulations: isotropic acoustic, TTI-acoustic, isotropic elastic, and VTI-elastic. To isolate inference cost, we do not train networks as the runtime depends on architecture, and not specific weight values. When TFNO and FD share the same spatial grid (10 m cells) but TFNO runs at the temporal Nyquist rate (coarser than the CFL-limited FD step), TFNO is consistently slower, by factors from 1.4x to 80x, across all physics. Allowing TFNO to operate on a Nyquist-rate spatial grid (2.5x coarser per dimension than FD) narrows the gap: small architectures (4-8 layers, 12-24 hidden channels) achieve up to 10x faster runtime (VTI-elastic), whereas larger networks (12 layers, 36 channels) produce mixed results: Elastic cases are 1.09x and 1.30x faster (isotropic and VTI, respectively), while TTI-acoustic and isotropic acoustic are 1.41x and 5.9x slower. A decisive advantage appears only in a "surface-only" configuration that predicts the boundary time history u(x,y,z=0,t): TFNO can be up to 4e3 faster than FD. Overall, TFNOs offer architecture-dependent gains and, for full-volume high-fidelity simulations at matched resolution, are generally slower than optimized FD; by contrast, for boundary-field predictions they can deliver orders-of-magnitude acceleration.