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.
authors: Lynton Ardizzone Jakob Kruse Carsten Rother Ullrich Köthe
hIndex: Carsten Rother 77