Effect of Equivariance in Uncertainty Quantification for Full-Wave Inverse Scattering

In this work, we compare an equivariance-based uncertainty quantification method with traditional uncertainty quantification methods for solving inverse scattering problem (ISP). By utilizing the equivariance property of certain transformations in ISP, a set of prediction results corresponding to the same input can be obtained and used for uncertainty quantification. By numerous tests, it is shown that uncertainty quantified by the equivariance-based method has significant higher correlation with the true error than the perturbation-based methods, such as Monte Carlo Dropout (MCD). It also achieves comparable performance with Deep-Ensemble, while it needs much less training and storage cost. Furthermore, reasons why equivariance perform well in uncertainty quantification is analyzed.