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math.NA2026
A Locally Conservative Enriched Linearized Neural Network Approximation to Elliptic PDEs
Seungil Kim, Gwanghyun Jo, Young Ju Lee
This paper presents a locally conservative Enriched Linearized Neural Network (ENN) method for the Darcy flow model. A linearized shallow ReLU network, whose hidden-layer param…
math.NA2026
Analysis of Error Propagation in Autoencoder-Based Reduced-Order Neural Ordinary Differential Equations
Jingyi Zhang, Gwanghyun Jo
Neural ODE reduced-order models often achieve comparable local prediction accuracy, yet their long-horizon extrapolation behavior can differ substantially. To analyze this discrepa…