Reproduce “RED-DiffEq: Regularization by denoising diffusion models for solving inverse PDE problems with application to full waveform inversion” on OpenResearch

About this paper

Siming Shan, Min Zhu, Youzuo Lin, Lu Lu

Researchers from Yale University and the University of North Carolina at Chapel Hill developed RED-DiffEq, a computational framework that integrates pretrained denoising diffusion models as a regularization mechanism into physics-driven inversion for PDE-governed inverse problems. The method demonstrated superior accuracy and robustness in reconstructing subsurface velocity models, including complex geological features, under conditions of noise, missing data, and out-of-distribution scenarios, while also providing uncertainty quantification.

Key insights

• Systematic integration of a learned, complex data-driven prior via diffusion models significantly enhances the accuracy, robustness, and geological realism of inverted models compared to traditional regularization methods.
• The combination of the diffusion-based regularization with a domain decomposition strategy enables strong generalization capabilities, allowing the framework to effectively tackle larger and out-of-distribution inverse problems.
• The stochasticity inherent in the diffusion-based regularization can be leveraged to provide meaningful uncertainty quantification (UQ) for the reconstructed solutions, correlating uncertainty with regions of structural complexity.

Summary by alphaXiv.