Residual-based error correction for neural operator accelerated infinite-dimensional Bayesian inverse problems

Lianghao Cao, Thomas O'Leary-Roseberry, Prashant K. Jha, J. Tinsley Oden, Omar Ghattas

Abstract: Highlights•Neural operators with error-correction as surrogate models for nonlinear PDEs.•The error in Bayesian inversion is controlled by the neural operator approximation error.•Correction via solving a linear variational problem defined by the PDE residual.•Correction leads to quadratic error reduction of the neural operator approximation error.•Significantly improved inference results from error-corrected neural operators.