"Learning Boundary Operators and Inverse Potential Problems"Jin ChengReconstructing the interior potential from boundary measurements represents a challenging class of inverse problems with significant theoretical and practical implications. The development of numerical algorithms for such inverse problems is a topic of considerable interest to both mathematicians and engineers. In this presentation, we will discuss our recent findings on learning the Robin-to-Dirichlet boundary operators and demonstrate how these operators can be utilized to reconstruct the potential function. Both our theoretical and numerical results indicate the effectiveness of our proposed methods. |
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