Alpha-VI DeepONet: A prior-robust variational Bayesian approach for enhancing DeepONets with uncertainty quantification

We introduce a novel deep operator network (DeepONet) framework that incorporates generalised variational inference (GVI) using Rényi's $α$-divergence to learn complex operators while quantifying uncertainty. By incorporating Bayesian neural networks as the building blocks for the branch and trunk networks, our framework endows DeepONet with uncertainty quantification. The use of Rényi's $α$-di…