From ICON to GenICON: In-Context Operator Learning with Uncertainty Quantification (Siting Liu, UCR)

Abstract: I will introduce In-Context Operator Networks (ICON), a framework in which a single neural network learns solution operators for differential equations directly from a few prompted input-output examples at inference time, without any weight updates. ICON acts as a few-shot learner across forward and inverse problems for ODEs, PDEs, and mean-field control. I will then present a probabilistic interpretation: under a random differential equation data model, ICON implicitly computes the posterior predictive mean given the context, linking operator learning to Bayesian inference. This motivates GenICON, a generative variant that samples from the posterior predictive for principled uncertainty quantification, yielding a unified Bayesian view of in-context operator learning.