Variational Autoencoder Inverse Mapper: An End-to-End Deep Learning Framework for Inverse Problems

Inverse problems - using measured observations to determine unknown parameters - are well motivated but challenging in many science and engineering problems. In this paper, we propose an end-to-end deep learning framework, the Variational Autoencoder Inverse Mapper (VAIM), as an autoencoder-based neural network architecture for inverse problems. The encoder and decoder neural networks approximate the forward and backward mapping, respectively, and a variational latent layer is incorporated into VAIM to learn the posterior parameter distributions with respect to given observables. We demonstrate the effectiveness of VAIM for several toy inverse problems, with both finite and infinite solutions, and for constructing the inverse function mapping quantum correlation functions to observables in a Quantum Chromodynamics analysis of nucleon structure.