On stability and regularization for data-driven solution of parabolic inverse source problems

Mengmeng Zhang, Qianxiao Li, Jijun Liu

Abstract: Highlights•We prove generalization error estimates depending on training errors and data noise levels by establishing conditional stability of the inverse problem. These generalization error estimates essentially reflect the stability due to both the model itself and the reconstruction algorithm.•We propose a new loss function involving the derivative of the residuals for PDE and measurement data, which can be understood as the regularizing penalty specified to the solution of inverse problems, dealing with the ill-posedness of the problem.•Using these regularization terms, we develop reconstruction scheme and demonstrate the effectiveness of our proposed methodology, which performs better in recovering the smooth unknown source.