Neumann series-based neural operator for solving 2D inverse medium problem

The inverse medium problem, inherently ill-posed and nonlinear, poses significant computational challenges. We adopt a physics-assisted approach, utilizing a neural operator as a surrogate solver for the forward problem to accelerate reconstruction. Existing neural network methods fail to effectively solve the forward problem when simultaneously handling source and scatterer parameters as inputs. To overcome this, we propose integrating a Neumann series structure to efficiently manage such multi-input scenarios. Extensive experimental results demonstrate the framework's superior computational efficiency, robust generalization, and adaptability, offering valuable insights for solving similar inverse problems.