Faster Uncertainty Quantification for Inverse Problems with Conditional Normalizing Flows

Understand

In inverse problems, we often have access to data consisting of paired samples $(x,y)\sim p_{X,Y}(x,y)$ where $y$ are partial observations of a physical system, and $x$ represents the unknowns of the problem.

• Under these circumstances, we can employ supervised training to learn a solution $x$ and its uncertainty from the observations $y$.
• We refer to this problem as the "supervised" case.
• However, the data $y\sim p_{Y}(y)$ collected at one point could be distributed differently than observations $y'\sim p_{Y}'(y')$, relevant for a current set of problems.