  Interpreting scattered acoustic and electromagnetic wave patterns is a
computational task that enables remote imaging in a number of important
applications, including medical imaging, geophysical exploration, sonar and
radar detection, and nondestructive testing of materials. However, accurately
and stably recovering an inhomogeneous medium from far-field scattered wave
measurements is a computationally difficult problem, due to the nonlinear and
non-local nature of the forward scattering process. We design a neural network,
called Multi-Frequency Inverse Scattering Network (MFISNet), and a training
method to approximate the inverse map from far-field scattered wave
measurements at multiple frequencies. We consider three variants of MFISNet,
with the strongest performing variant inspired by the recursive linearization
method -- a commonly used technique for stably inverting scattered wavefield
data -- that progressively refines the estimate with higher frequency content.
