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This paper proposes structure-preserving neural surrogates for partial differential equations that integrate Gaussian process regression to provide tractable uncertainty quantification, enabling real-time simulation with closed-form error estimates.
This paper introduces the Iterative Refinement Neural Operator (IRNO), which augments pretrained neural operators with a learned refinement module applied via fixed-point iteration to mitigate spectral bias. IRNO progressively corrects high-frequency errors, achieving up to 56% improvement on turbulent flow and showing stable extrapolation beyond the trained iteration count.