CuWave

CuWave is a GPU-accelerated (single or multi), differentiable finite difference wave propagation code. Possible applications include

nondestructive testing via full waveform inversion
transient acoustic topology optimization
analog neural networks
transient photonic topology optimization

Documentation

• see the documentation for how the code works (AI-assisted; verify with sources for critical details)
• see examples for how to apply the code

Multiple GPUs

Several GPUs take one argument, and the driver otherwise stays as it is:

• Simulation(..., devices=(0, 1)) splits one grid along its first axis over the listed GPUs, for grids too large or too slow for one. simulate, sensitivity, reconstruction_sensitivity and superposition_sensitivity then run split and return the same result as on one GPU, bitwise. Try it with the DEVICES setting of
  • examples/forward/scalarND.py, the forward problem in 2D or 3D
  • examples/sensitivity/scalar2D_sensitivity.py, the gradient
• misfit_gradient(..., devices=[0, 1]) (and measure, misfit) deals the shots of an inversion out over the GPUs, which needs no communication and is the faster choice whenever one shot fits one GPU.

Development status

Scalar & acoustic wave equations have been developed over the last 2 years and are thoroughly validated. The elastic wave and electromagnetic wave equations were developed with AI assistance (Claude). The first is validated on experimental data, while the latter are cross-validated against the independent FDTD code FDTDX.

Performance

CuWave's runtime for identical discretizations is comparable to that of other established wave propagation finite difference codes. Speedups in 2D with reflecting boundaries (a ratio above 1 means CuWave is that many times faster) compared to the following frameworks:

• scalar wave equation
  • Deepwave (forward: ~1.1x, sensitivity: ~1x)
  • NVIDIA Warp (forward: ~2.1x, sensitivity: ~1.8x)
  • SeismicWaves.jl (forward: ~4.4x, sensitivity: ~4x)
  • Devito on CPU (forward: ~3.6x, sensitivity: ~3.8x)
• elastic wave equation
  • Deepwave (forward: ~1.1x, sensitivity: ~1.3x)
  • SeismicWaves.jl (forward: ~4x, sensitivity: ~5x) Tested on one NVIDIA RTX PRO 500 Blackwell laptop GPU (6 GB) on the largest possible grids with CuWave's superposition_sensitivity as reference for the sensitivities. The specific numbers need to be taken with a grain of salt, as they are subject to specific hardware and simulation setup. All implementations operate on the same order of magnitude.

Additional benefits of CuWave are

• the built-in higher order finite difference schemes, allowing for fewer grid points
• a sensitivity analysis whose memory is independent of the number of timesteps, allowing for orders of magnitude larger grids

Install

pip install cuwave

Requires an NVIDIA GPU and CuPy matching your CUDA toolkit (e.g. pip install cupy-cuda12x), which is not pulled in automatically. For the full installation, including the optional PyTorch and running the tests, see docs/install.md.

References

If you use our code for your scientific research, please acknowledge this by referring to the following publication:

Herrmann, L., Bürchner, T., Kudela, L., Kollmannsberger, S., 2026, A memory-efficient adjoint method to enable billion parameter optimization on a single GPU in dynamic problems, Structural and Multidisciplinary Optimization, Volume 69, 52 (2026), DOI: 10.1007/s00158-025-04237-y

Acknowledgements

Ideas adapted from FDTDX (Mahlau, Schubert, Berg & Rosenhahn 2026), which also serves as the reference for validating the electromagnetic solvers.

Contact

For questions, bug reports, or collaboration inquiries, please don't hesitate to contact Leon Herrmann at herrmann.leon@pm.me.

License

MIT; see LICENSE.