Beyond Spatial Prediction: Nonlinear Output Representations for Inverse Scattering

Inverse scattering problems represent a severely ill-posed regime where the spatially varying contrast of a medium is recovered from measurements of the scattered wavefield. Typically, machine-learning approaches output reconstructions in a discretized spatial parametrization, where the neural networks predict the contrast at each grid point. In this paper, we study this output choice and build a modular head which reconstructs the contrast field through a learned, lower-dimensional nonlinear parametrization, replacing spatial parametrizations. The network therefore predicts latent coordinates, whose space carries our prior on the structure of our contrast fields. Across three target distributions, three noise levels, and multiple seeds, pretrained latent decoding reduces normalized mean squared error by an average of 34% relative to the spatial-output variants of five leading neural-operator architectures. The gain holds in fairly matched studies, including controls on parameter counts, MACs, and training recipes. In one setting, we observe that a spatial network with $7\times$ the trainable parameters needs a longer training schedule just to reach parity with a nonlinear latent head. We also study the impact of nonlinearity, finding the largest gain over linear latents for sharp contrast fields and less for smooth low-rank fields. Our results show that nonlinear latents serve as a strong representation space for learned inverse scattering methods.