应兰州大学数学与统计学院邀请，上海交通大学数学科学学院燕雄斌博士将于2024年9月26日上午举行线上学术报告。

报告题目:ODE-DPS: ODE-based Diffusion Posterior Sampling for Linear Inverse Problems in Partial Differential Equation

报告摘要：In recent years we have witnessed a growth in mathematics for deep learning, which has been used to solve inverse problems of partial differential equations (PDEs). However, most deep learning-based inversion methods either require paired data or necessitate retraining neural networks for modifications in the conditions of the inverse problem, significantly reducing the efficiency of inversion and limiting its applicability. To overcome this challenge, in this paper, leveraging the score-based generative diffusion model, we introduce a novel unsupervised inversion methodology tailored for solving inverse problems arising from PDEs. Our approach operates within the Bayesian inversion framework, treating the task of solving the posterior distribution as a conditional generation process achieved through solving a reverse-time stochastic differential equation. Furthermore, to enhance the accuracy of inversion results, we propose an ODE-based Diffusion Posterior Sampling inversion algorithm. The algorithm stems from the marginal probability density functions of two distinct forward generation processes that satisfy the same Fokker-Planck equation. Through a series of experiments involving various PDEs, we showcase the efficiency and robustness of our proposed method.

时 间：9月26日（星期四）10：00-11:00

腾讯会议ID：168-810-984

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燕雄斌博士简介

燕雄斌，2022年博士毕业于兰州大学，现为上海交通大学数学科学学院博士后，在JIIP, CMAME, JCAM等期刊上发表SCI论文十余篇，主持国家自然科学基金1项。

甘肃应用数学中心

甘肃省高校应用数学与复杂系统省级重点实验室

数学与统计学院

萃英学院

2024年9月24日