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This paper presents a comprehensive mathematical framework for sequential surrogate modeling of three-phase black-oil reservoir dynamics using Fourier Neural Operators (FNO) and physics-informed variants (PINO), applied to the Norne benchmark reservoir. Theoretical contributions include functional-analytic formulation, covariate shift analysis, physics-constrained spectral stability, and truncated backpropagation gradient analysis.
Fourier neural operators (FNOs) achieve extrapolation success in modeling periodically driven quantum systems, capturing temporal correlations in frequency space for physically faithful dynamics beyond training data.
This paper investigates the generalization behavior of Fourier Neural Operators and Deep Operator Networks under distribution shifts in a variable-coefficient wave equation, revealing that FNO struggles with high-frequency inputs while DeepONet shows milder degradation.