LINEARIZED INVERSE SCHRODINGER POTENTIAL PROBLEM WITH PARTIAL DATA AND ITS DEEP NEURAL NETWORK INVERSION

作者：Zou, Sen^*; Lu, Shuai^*; Xu, Boxi^*

来源：Inverse Problems and Imaging, 2022.

DOI：10.3934/ipi.2022045

• Inverse Schrodinger potential problem
• increasing stability
• lineariza-tion method
• partial boundary data
• deep neural network

We study the linearized inverse Schro center dot dinger potential problem with (many) partial boundary data. By fixing specific partial boundary these measurements are realized by the linearized local Dirichlet-to-Neumann map. When the wavenumber is assumed to be large, we verify a Ho center dot lder type increasing stability by constructing the complex exponential solutions in a reflection form. Meanwhile, the linearized inverse Schro center dot dinger potential problem admits an integral equation where the unknown potential function is indirectly contained there. Such a formulation allows us to adopt a deep neural network inversion algorithm. Numerical examples show that one can reconstruct the unknown potential function stably within the partial boundary data setting.

• 单位
  复旦大学