Validation, GPU evidence and FAQ¶

SimpleFWI is research software with explicit numerical evidence and limits. The recorded suite at source revision abbfe1f passed 463 CPU tests and 10 separate CUDA tests on an NVIDIA A40. These counts describe the tests/fwi2d selection at that revision, not a blanket certification of the legacy repository, all hardware or full-scale recovery.

Reproducible validation records¶

CPU checks include adjoints and second derivatives, physical fixtures, all 15 optimizer recipes, multiscale transitions, recording and restart. CUDA checks include waveform and physical-gradient comparisons, small inversion, PML/free-surface multiscale parity and bounded recording. The hardware record does not certify every native optimizer or all precisions on GPU.

Reproduce the selections in the appropriate installed environment:

# CPU reference suite
OPENBLAS_NUM_THREADS=1 OMP_NUM_THREADS=1 \
  python -m pytest tests/fwi2d -m 'not cuda' -q

# Actual CUDA hardware required; skipped tests are not GPU evidence
python -c "import torch; assert torch.cuda.is_available(), 'CUDA device required'"
OPENBLAS_NUM_THREADS=1 OMP_NUM_THREADS=1 \
  python -m pytest tests/fwi2d -m cuda -q -rs

What the small Marmousi experiment shows¶

Every continuation stage ended below its initial data loss. However, final velocity RMSE was 34.8429 m/s, compared with 33.4132 m/s for the initial constant truth-mean model. Improved data fit did not improve model error in this short experiment.

The matched inversion took 1.03665 s on CPU direct and 13.07533 s on GPU FGMRES, with 17,673,728 peak allocated CUDA bytes. These are single measurements on a small crop with short, uncalibrated PML. They establish numerical workflow parity, not GPU speedup, large-survey memory scaling, independent continuum accuracy or high-frequency full Marmousi recovery.

The full validation guide also records harder iterative convergence failures and pre-existing legacy whole-repository pytest collection failures. A low linear residual or a passed dispersion screen alone does not establish physical accuracy.

Frequently asked questions¶

What is SimpleFWI?¶

SimpleFWI is an MIT-licensed Python research library for 2D constant-density acoustic frequency-domain full-waveform inversion in PyTorch. Its API combines Helmholtz modeling, adjoint gradients, bounded native optimization and local curvature analysis.

Can SimpleFWI run full-waveform inversion on a GPU?¶

Yes. The experimental CUDA FGMRES path passed ten numerical tests on an NVIDIA A40, including small inversion and multiscale comparisons. CPU sparse-direct solves remain the reference default. Large-scale high-frequency performance and GPU speedup are unestablished.

Does SimpleFWI use PML and support a free surface?¶

Yes. It pads the physical grid with stretched-coordinate PML. An optional flat pressure-release free surface replaces the top PML; side and bottom PML remain. PML thickness and damping require calibration for the chosen grid and frequency. See Helmholtz and PML.

How do multi-resolution and multi-frequency FWI differ?¶

Multi-resolution changes the grid; multi-frequency continuation changes the frequencies in the objective. SimpleFWI schedules both, transfers physical squared slowness on refinement and creates fresh optimizer state per stage. See the Marmousi continuation example.

Can I use PyTorch optimizers and compute a Hessian?¶

Yes. The runner integrates native PyTorch optimizer recipes; fifteen CPU recipes are tested with their documented constraints. Exact and Gauss–Newton Hessian-vector products avoid dense Hessian assembly. Local uncertainty also requires noise scaling, declared parameter coordinates and a proper prior. See Hessian and uncertainty.

What wave physics and problem sizes are supported?¶

The current API is 2D, constant-density and acoustic, with a flat optional free surface. It does not implement 3D, elastic or variable-density inversion. The recorded GPU experiments use small fixtures and crops; full-model high-frequency scalability remains unverified.

How should I cite or report a SimpleFWI result?¶

Attribute the repository and contributors, record the exact revision and numerical configuration, and retain the MIT license notice. Include dataset provenance, noise/weight assumptions, model coordinates, device, precision and solver tolerances. No associated publication or DOI is claimed by these pages.