用预训练扩散模型做正则化，提升地震反演的精度与鲁棒性。
RED-DiffEq: Regularization by denoising diffusion models for solving inverse PDE problems with application to full waveform inversion
- 用扩散模型作为先验正则化，融合物理规律与数据驱动。
- 在复杂速度模型上仍保持高精度，比传统方法更稳定。
- 适用于多种偏微分方程反问题，尤其适合噪声敏感场景。
偏微分方程（PDE）约束的反问题在众多科学与工程领域中至关重要，但受非线性、不适定性和对噪声敏感等挑战困扰。本文提出RED-DiffEq新框架，结合物理驱动反演与数据驱动学习，利用预训练扩散模型作为PDE反问题的正则化机制。将该方法应用于地球物理学中的全波形反演（FWI），这是一种旨在从地震观测数据重建高分辨率地下速度模型的挑战性成像技术。实验表明，相比传统方法，该方法显著提升了准确率与鲁棒性，并展现出对未训练过的复杂速度模型的强大泛化能力。该框架可直接推广至多种PDE约束的反问题。
原文摘要 · Abstract (English)
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.
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