Uncertainty Quantification and Calibration in Full-Wave Inverse Scattering Problems With Evidential Neural Networks

Abstract

Recently, deep learning-based solvers for inverse scattering problems (ISPs) have been continuously developed. The ill-posedness and nonlinear nature of ISPs make deep learning-based ISP solvers sensitive to input data and prone to generalization issues, thus necessitating uncertainty quantification (UQ) and calibration. Conventional methods for UQ and calibration of deep learning-based ISP solvers primarily include deep ensemble and dropout-based methods based on Bayesian neural networks (BNNs). However, these methods require extra steps to generate multiple predictions for estimating model uncertainty. In addition, these BNN-based methods are sensitive to prior selection and may yield unsatisfactory calibration performance. This article proposes an evidential deep learning scheme (EDLS) to solve ISPs and obtain pixelwise and better-calibrated uncertainty estimates with lower computational cost. To evaluate the performance of uncertainty calibration, we use calibration curves to assess the consistency between expected and observed confidence levels. Comparative experiments with deep ensemble and Monte Carlo dropout (MC-Dropout) demonstrate that EDLS exhibits advantages in reconstruction accuracy and uncertainty calibration quality, providing uncertainty estimates that are most consistent with prediction errors. EDLS offers a real time, calibrated, and scalable approach for obtaining ISP reconstruction results and reliable uncertainty estimates.