Geometry-Aware Post-Hoc Uncertainty Quantification in Operator Learning

The article introduces REEF-GP (Residual on Embedded Features Gaussian Process), a novel post-hoc uncertainty quantification (UQ) framework designed for neural operators used in solving partial differential equations (PDEs). By fitting a Gaussian Process to the residuals of a frozen neural operator, REEF-GP leverages the operator's intrinsic coordinate-feature representations to create geometry-aware uncertainties, achieving calibrated uncertainty estimates across five PDE benchmarks while maintaining predictive accuracy and scalability. This method addresses the limitations of existing parameter-centric UQ approaches, making it a valuable tool for practitioners needing reliable uncertainty quantification in complex geometrical contexts.