学术报告

题      目： Geometric Inverse Problems Meet Operator Learning

报  告  人：郭汝驰   助理教授  (邀请人：钟柳强 )

                                  加州大学欧文分校

时      间：2022-10-12 15:00-17:00

地      点：西楼二楼会议室 

报告人简介:

       郭汝驰，美国加州大学 Irvine分校助理教授，主要从事浸入有限元方面的研究，目前已发表论文十 余篇，论文发表在SIAM Journal of Numerical Analysis、SIAM Journal on Scientific Computing、Journal of Computational Physics期刊上。

摘      要：

       Geometric Inverse Problems are of great importance in practice which aims to recover the internal medium structure by boundary data. Typical examples include electrical impedance tomography (EIT) and Diffuse Optical Tomography (DOT) which are promising techniques for non-invasive and radiation-free-type of medical imaging. Mathematically, the forward problems are modeled by partial differential equations (PDEs) and the considered inverse problem is to recover the PDE coefficients. A high-quality reconstruction is always challenging due to its severe ill-posedness. Based on the idea of direct sampling methods (DSMs), we present a framework to construct deep neural networks for solving these inverse problems. It is able to capture the underlying mathematical structure. The resulting Deep DSM (DDSM) is easy for implementation, and its offline-online decomposition inherits efficiency from the original DSM that does not need any optimization process in reconstruction. Additionally, it is capable of systematically incorporating multiple Cauchy data pairs to achieve high-quality reconstruction and is also highly robust to large noise.