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

TL;DR

This paper critically evaluates the speed claims of Fourier Neural Operators for wave propagation, finding they are generally slower than optimized finite-difference methods for full-volume simulations but can be vastly faster for boundary predictions.

Contribution

It provides a comprehensive benchmarking of Tucker-tensorized FNOs against GPU-accelerated finite-difference codes across multiple wave physics formulations, clarifying their true performance advantages.

Findings

FNOs are slower than FD at same spatial resolution.

FNOs can be faster when operating on coarser spatial grids.

Boundary predictions with FNOs are significantly faster than FD.

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.