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.
To analyze inverse problems with Invertible Neural Networks The author proposes to use invertible networks to solve ambiguous inverse problems and suggest to not only train the forward model, but also the inverse model with an MMD critic. The research paper proposes an invertible network with observations for posterior probability of complex input distributions with a theoretical valid bidirectional training scheme.
