Analyzing Inverse Problems with Invertible Neural Networks
For many applications, in particular in natural science, the task is todetermine 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 canresult in the same measurement.To fully characterize this ambiguity, the fullposterior parameter distribution, conditioned on an observed measurement,has to be determined.We argue that a particular class of neural networksis well suited for this task – so-called Invertible Neural Networks.Unlike classical neural networks, which attempt to solve the ambiguousinverse problem directly, INNs focus on learning the forward process, usingadditional latent output variables to capture the information otherwiselost.Due to invertibility, a model of the corresponding inverse process islearned implicitly.Given a specific measurement and the distribution ofthe latent variables, the inverse pass of the INN provides the full posteriorover parameter space.We prove theoretically and verify experimentally, onartificial data and real-world problems from medicine and astrophysics, thatINNs 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 NetworksThe 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.