Title: RED-DiffEq: Regularization by denoising diffusion models for solving inverse PDE problems with application to full waveform inversion Show Chinese title

Title: RED-DiffEq：用于解决逆PDE问题的去噪扩散模型正则化方法及其在全波形反演中的应用

Abstract: 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. Show Chinese abstract

Abstract: 偏微分方程（PDE）主导的反问题在各种科学和工程应用中是基础性的；然而，由于非线性、不适定性和对噪声的敏感性，它们面临重大挑战。 在这里，我们通过整合物理驱动的反演和数据驱动的学习，引入了一个新的计算框架，RED-DiffEq。 RED-DiffEq利用预训练的扩散模型作为PDE主导的反问题的正则化机制。 我们将RED-DiffEq应用于地球物理学中的全波形反演问题，这是一种具有挑战性的地震成像技术，旨在从地震测量数据中重建高分辨率地下速度模型。 与传统方法相比，我们的方法显示出更高的准确性和鲁棒性。 此外，它对扩散模型未训练过的更复杂的速度模型表现出强大的泛化能力。 我们的框架也可以直接应用于各种PDE主导的反问题。