seminar

The focus of this talk is on the numerical methods used to identify parameters in partial differential equations. Typically, an optimization approach is used to solve this class of inverse problems, which is then discretized using finite difference method, finite element methods, or deep neural networks for practical purposes. Then one critical issue is to establish a priori error estimates for the numerically reconstructed parameter. In this talk, the speaker will discuss their recent study on the deep neural network approximation for parameter identification problems by effectively utilizing relevant stability results.