Title: Analyzing Inverse Problems with Invertible Neural Networks. Abstract: For many applications, in particular in natural science, the task is to
determine hidden system parameters from a set of measurements. Often,
the forward process from parameter- to measurement-space is well-defined,
whereas the inverse problem is ambiguous: multiple parameter sets can
result in the same measurement. To fully characterize this ambiguity, the full
posterior parameter distribution, conditioned on an observed measurement,
has to be determined. We argue that a particular class of neural networks
is well suited for this task – so-called Invertible Neural Networks (INNs).
Unlike classical neural networks, which attempt to solve the ambiguous
inverse problem directly, INNs focus on learning the forward process, using
additional latent output variables to capture the information otherwise
lost. Due to invertibility, a model of the corresponding inverse process is
learned implicitly. Given a specific measurement and the distribution of
the latent variables, the inverse pass of the INN provides the full posterior
over parameter space. We prove theoretically and verify experimentally, on
artificial data and real-world problems from medicine and astrophysics, that
INNs are a powerful analysis tool to find multi-modalities in parameter space,
uncover parameter correlations, and identify unrecoverable parameters.