Seismic Wavefield Simulation Benchmark

When Do Neural Approaches Outperform Finite Differences for Seismic Wavefield Simulation?

A systematic benchmark comparing PINNs, FNOs, and classical FD solvers for the 2D acoustic wave equation across 5 to 80Hz.

Author: Manish Paul, IIT Kharagpur | Paper: arXiv pending | Code: fully reproducible

Key Findings

FD is fast, accurate, and frequency-independent - solves all frequencies in under 25ms with machine precision regardless of velocity model complexity.

PINNs fail at every frequency - spectral bias causes IC loss to stagnate at 0.76, producing slowdowns of 1814x to 2909x and amplitude errors exceeding 26000x relative to FD.

FNO works at low frequencies - achieves 0.91% L2 error at 5Hz and 1.79% at 10Hz on homogeneous media.

FNO fails above 10Hz due to amplitude degeneracy - a previously undocumented failure mode where near-uniform wavefield amplitudes flatten the MSE loss surface.

FNO degrades on layered media - L2 error increases 36-fold at 5Hz and fails completely at 10Hz, even with model-specific retraining.

Results Summary

Method	5Hz	10Hz	20Hz	40Hz	80Hz
FD	under 25ms	under 25ms	under 25ms	under 25ms	under 25ms
FNO homogeneous	0.91% L2	1.79% L2	FAIL	FAIL	FAIL
FNO layered	32.4% L2	FAIL	-	-	-
PINN	2132x	1814x	1829x	2178x	2909x

Setup

pip install torch numpy matplotlib deepxde neuraloperator

All experiments run on Apple M1 MacBook Air 8GB RAM with MPS acceleration.

Reproducing Results

python3 fd_solver/frequency_benchmark.py
python3 pinn_solver/pinn_frequency_sweep.py
python3 fno_solver/fno_v2.py
python3 fno_solver/fno_layered.py
python3 notebooks/visualisation.py

Paper

Title: When Do Neural Approaches Outperform Finite Differences for Seismic Wavefield Simulation? A Systematic Comparison of PINNs, Fourier Neural Operators, and Classical Solvers

Full paper in paper/main.tex. All 8 citations verified. PDF available on request.

Citation

@misc{paul2026seismic,
  title={When Do Neural Approaches Outperform Finite Differences for Seismic Wavefield Simulation?},
  author={Paul, Manish},
  year={2026},
  institution={Indian Institute of Technology Kharagpur},
  note={arXiv preprint, identifier pending}
}

License

MIT License.