ifwi-pub

Reproducible synthetic examples for two companion papers by Shaowen Wang and Tariq Alkhalifah:

Accelerating High Resolution Implicit Full Waveform Inversion (Geophysics)
— the single-parameter velocity examples (Overthrust, Marmousi)

Implicit Full Waveform Inversion Imaging (GJI, 2026) — DOI 10.1093/gji/ggag277
— the joint velocity–impedance imaging (IFWIM) example (Marmousi2)

All forward/adjoint modeling runs on the sweep differentiable acoustic solver. The two single-parameter notebooks each reproduce one Geophysics experiment — three inversions on one model and the comparison figures — and the multiparameter notebook reproduces the joint $(v_p, Z)$ imaging example of the GJI paper:

Notebook	Model	Experiments
notebooks/pseudo_hessian_overthrust.ipynb	Overthrust	conventional FWI · iFWI (SIREN) · iFWI + pseudo-Hessian
notebooks/hash_encoding_marmousi.ipynb	Marmousi	conventional FWI · iFWI (SIREN) · iFWI + hash encoding
notebooks/multiparameter_marmousi2.ipynb	Marmousi2	joint $(v_p, Z)$ implicit FWI imaging (variable density, hash + multiscale)

The two single-parameter methods (which the Geophysics paper builds on) were first presented as EAGE extended abstracts, reproduced here:

• Implicit full waveform inversion with energy-weighted gradient — DOI 10.3997/2214-4609.202510069 (pseudo-Hessian / Overthrust)
• Multiresolution hash encoding for high resolution implicit full waveform inversion — DOI 10.3997/2214-4609.202510109 (hash encoding / Marmousi)

The multiparameter Marmousi2 notebook reproduces the joint velocity–impedance imaging example of the GJI paper Implicit Full Waveform Inversion Imaging (DOI 10.1093/gji/ggag277).

Method

The velocity model is reparameterized by a coordinate network and inverted through the wave equation:

vp(grid) = vp_init + std · net(coords) + mean

• Conventional FWI optimizes the grid velocity directly.
• Implicit FWI (iFWI) makes net a SIREN MLP (the paper's baseline).
• Pseudo-Hessian preconditions the velocity-grid gradient by the source/receiver illumination — g ← g / sqrt(s·r) — before back-propagating it into the network. s and r are read directly off the sweep solver (solver.source_illumination / solver.receiver_illumination). The compiled backend fills them only when the extra grid pass is requested with solver.compute_illumination = True — it has been opt-in since sweep 2026-06, and run_inversion sets it for you whenever use_ph=True. (Overthrust example.)
• Hash encoding prepends a native Instant-NGP multiresolution hash-grid encoder to the SIREN. (Marmousi example.)
• Multiparameter imaging (FWIM) inverts velocity and impedance jointly with a single shared hash + SIREN network (model_i = init_i + std_i · net(coords)[i]), driven by the variable-density AcousticVRZ solver. A band-pass multiscale schedule (3, 5, 8, all Hz) restarts the network + optimizer at each scale, baking the previous scale's model into the init. (Marmousi2 example.) Reproduction detail: the zero-phase band-pass must be a time-domain filtfilt (torchaudio, fp64) — a frequency-domain |H|² multiply leaves a coherent t=0 wrap artefact that destabilises the joint inversion.

Everything except the wave solver is implemented from scratch in src/ifwi_sweep.py: the SIREN network, the multiresolution hash encoding (pure PyTorch — not tinycudann) and the pseudo-Hessian preconditioner. The notebooks depend only on sweep plus torch / numpy / matplotlib.

Solver settings

All forward/adjoint modeling uses the compiled CUDA backend with boundary saving:

solver = PropTorch(Acoustic(spatial_order=..., device="cuda"), shape, dh, dt,
                   abcn=..., source_type=["h1"], receiver_type=["h1"], impl="c")
solver.compute_illumination = True   # pseudo-Hessian only (run_inversion sets this for you)
syn = solver(wavelet, sources, receivers, models=[vp], use_boundary_saving=True)  # 'bs' mode

Boundary saving is already the impl='c' default, so the use_boundary_saving=True above is explicit rather than necessary. Since sweep 0.2.0 the gradient-memory mode is one three-way choice and the documented spelling is PropTorch(..., memory=MemoryOptions(strategy="boundary")) (from sweep.propagator.options import MemoryOptions); the legacy switch used here resolves to the same mode. If the boundary ring does not fit your GPU, pass BoundaryOptions(storage="cpu") inside it.

free_surface= must be a constructor argument (the multiparameter notebook uses free_surface=True): sweep 0.2.0 rejects setting it after construction, because the padded grid and the compiled kernels are fixed at build time.

Layout

src/ifwi_sweep.py     solver wiring + SIREN + hash encoding + pseudo-Hessian + VRZ restart + filters
src/models.py         Overthrust/Marmousi vp and Marmousi2 vp+impedance, true/smooth, embedded (zlib+base85)
notebooks/            pseudo_hessian_overthrust + hash_encoding_marmousi + multiparameter_marmousi2
figures/              comparison figures written by the notebooks (and cached results, gitignored)
tools/encode_models.py  regenerates src/models.py from .npy (only needed to update the models)

Installation

A CUDA GPU is required — this repo drives the solver with impl='c' (the compiled CUDA path). Install the sweep differentiable solver from PyPI:

pip install "sweep-solver>=0.2,<0.3"            # provides the `sweep` package
python -c "import sweep; sweep.precompile()"    # build the CUDA backend now (one-time, ~3-5 min)

The solver ships the CUDA sources and compiles them against your own PyTorch, for your GPU's architecture only, then caches the result in ~/.cache/torch_extensions. That needs nvcc >= 12.4 (a system install, your cluster's module load cuda, or conda install -c nvidia cuda-toolkit). The precompile() line does the build up front; drop it and it happens — silently, for several minutes — inside the first notebook cell that calls the solver. Without a usable nvcc the solver falls back to the pure-PyTorch impl='eager' path with a warning: that is 10-30x slower and has no illumination, so the pseudo-Hessian experiment cannot run there. The notebooks print solver.impl; check it says c. pip install sweepx installs the same solver through the umbrella distribution, plus the sweep-agent companion this repo does not use. Full notes are in the sweep docs.

The notebooks additionally need torch numpy scipy matplotlib jupyter (all present in a sweep environment; see requirements.txt); the multiparameter notebook also uses torchaudio for the zero-phase band-pass filtfilt. No model data files are needed — the velocity models are embedded in src/models.py.

Running

With sweep installed, run the notebooks:

cd notebooks
jupyter lab            # open a notebook and run all cells

The notebooks ship with SMOKE = False (the full paper run — Overthrust 500 iterations, Marmousi 200, Marmousi2 400 = 4 scales × 100). Set SMOKE = True in the config cell for a quick reduced-iteration check (or set IFWI_EPOCHS). Inversion results are cached under figures/cache_*.npz, so re-running only re-plots (seconds) — delete the cache, or change any config value, to recompute. Observed data is generated on the fly by the same solver, so no pre-computed data is needed.

The cache key is the config signature only, not the solver version: a cache written by an older sweep is replayed verbatim, and the notebook prints [cache] loaded ... when that happens. After upgrading the solver, delete figures/cache_*.npz so the inversions actually re-run.

License

Released under the MIT License — see LICENSE.

Citation

If this repository is useful in your research, please cite the relevant paper(s):

Journal articles

• S. Wang and T. Alkhalifah, Implicit Full Waveform Inversion Imaging — Geophysical Journal International, 2026 — DOI 10.1093/gji/ggag277 (multiparameter IFWIM / Marmousi2)
• S. Wang and T. Alkhalifah, Accelerating High Resolution Implicit Full Waveform Inversion — Geophysics (under review) — single-parameter velocity: pseudo-Hessian + hash encoding

Conference abstracts

• S. Wang and T. Alkhalifah, Implicit full waveform inversion with energy-weighted gradient — EAGE Annual Conference & Exhibition, 2025 — DOI 10.3997/2214-4609.202510069 (pseudo-Hessian / Overthrust)
• S. Wang, M. Ravasi and T. Alkhalifah, Multiresolution hash encoding for high resolution implicit full waveform inversion — EAGE Annual Conference & Exhibition, 2025 — DOI 10.3997/2214-4609.202510109 (hash encoding / Marmousi)
• S. Wang and T. Alkhalifah, Accelerating the convergence of implicit FWI and LSRTM with a field data application — International Meeting for Applied Geoscience & Energy (IMAGE), 2025 — DOI 10.1190/image2025-4302395.1

Solver

• S. Wang and T. Alkhalifah, SWEEP: A Unified Solver Framework for Differentiable Wave Physics — arXiv 2604.14189

BibTeX

@misc{wang2026sweep,
  title  = {{SWEEP} ({S}eismic {W}ave {E}quation {E}xploration {P}latform):
            A Unified Solver Framework for Differentiable Wave Physics},
  author = {Wang, Shaowen and Alkhalifah, Tariq},
  year   = {2026},
  eprint = {2604.14189},
  archivePrefix = {arXiv},
  url    = {https://arxiv.org/abs/2604.14189},
}

@article{wang2026imaging,
  author  = {Wang, Shaowen and Alkhalifah, Tariq},
  title   = {Implicit Full Waveform Inversion Imaging},
  journal = {Geophysical Journal International},
  year    = {2026},
  doi     = {10.1093/gji/ggag277}
}

@article{wang_accelerating,
  author  = {Wang, Shaowen and Alkhalifah, Tariq},
  title   = {Accelerating High Resolution Implicit Full Waveform Inversion},
  journal = {Geophysics},
  note    = {Under review}
}

@inproceedings{wang2025energyweighted,
  author    = {Wang, Shaowen and Alkhalifah, Tariq},
  title     = {Implicit Full Waveform Inversion with Energy-Weighted Gradient},
  booktitle = {EAGE Annual Conference \& Exhibition},
  year      = {2025},
  doi       = {10.3997/2214-4609.202510069}
}

@inproceedings{wang2025hash,
  author    = {Wang, Shaowen and Ravasi, Matteo and Alkhalifah, Tariq},
  title     = {Multiresolution Hash Encoding for High Resolution Implicit Full Waveform Inversion},
  booktitle = {EAGE Annual Conference \& Exhibition},
  year      = {2025},
  doi       = {10.3997/2214-4609.202510109}
}

@inproceedings{wang2025lsrtm,
  author    = {Wang, Shaowen and Alkhalifah, Tariq},
  title     = {Accelerating the Convergence of Implicit {FWI} and {LSRTM} with a Field Data Application},
  booktitle = {International Meeting for Applied Geoscience \& Energy (IMAGE)},
  year      = {2025},
  doi       = {10.1190/image2025-4302395.1}
}