RED-DiffEq: Regularization by denoising diffusion models for solving inverse PDE problems with application to full waveform inversion
This addresses ill-posed inverse problems in scientific and engineering domains like seismic imaging, offering a hybrid approach that is incremental in combining existing techniques.
The paper tackles the challenge of solving PDE-governed inverse problems, such as full waveform inversion in geophysics, by introducing RED-DiffEq, a framework that uses pretrained diffusion models for regularization, resulting in enhanced accuracy and robustness compared to conventional methods, with strong generalization to unseen complex models.
Partial differential equation (PDE)-governed inverse problems are fundamental across various scientific and engineering applications; yet they face significant challenges due to nonlinearity, ill-posedness, and sensitivity to noise. Here, we introduce a new computational framework, RED-DiffEq, by integrating physics-driven inversion and data-driven learning. RED-DiffEq leverages pretrained diffusion models as a regularization mechanism for PDE-governed inverse problems. We apply RED-DiffEq to solve the full waveform inversion problem in geophysics, a challenging seismic imaging technique that seeks to reconstruct high-resolution subsurface velocity models from seismic measurement data. Our method shows enhanced accuracy and robustness compared to conventional methods. Additionally, it exhibits strong generalization ability to more complex velocity models that the diffusion model is not trained on. Our framework can also be directly applied to diverse PDE-governed inverse problems.