Variational Objectives for Amortized Bayesian Inference in Inverse Problems: The Role of Posterior Conditioning

This research examines three variational objectives for amortized Bayesian inference using variational autoencoders (VAEs) in inverse problems: reverse KL formulation (VAE-KL), asymmetric Jensen-Shannon formulation (VAE-JS), and Jensen-Shannon formulation. The study specifically investigates how the choice of variational regularization affects posterior accuracy, with particular focus on weakly identified parameter directions in inverse problems. The work provides insights into selecting appropriate training objectives when applying amortized inference methods to physics-based inverse problems.