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cs.LG2026
Generalization Error Bounds for Picard-Type Operator Learning in Nonlinear Parabolic PDEs
Koichi Taniguchi, Sho Sonoda
Operator learning for partial differential equations (PDEs) aims to learn solution operators on infinite-dimensional function spaces from finite-resolution data. In this setting, i…
cs.LG2024
Quantitative Approximation for Neural Operators in Nonlinear Parabolic Equations
Takashi Furuya, Koichi Taniguchi, Satoshi Okuda
Neural operators serve as universal approximators for general continuous operators. In this paper, we derive the approximation rate of solution operators for the nonlinear paraboli…