Empirical Error Decomposition and Reliability Indicators for Neural Reduced-Order Models of Parametric PDEs

This paper develops an empirical error decomposition and reliability-indicator framework for neural reduced-order models of parametric partial differential equations. The framework separates errors associated with Proper Orthogonal Decomposition (POD) projection from errors introduced by neural prediction of reduced coordinates, enabling more interpretable assessment of reduced-order model reliability. Numerical experiments evaluate relative state error, POD projection error, neural reduced-coordinate prediction error, and empirical reliability indicators across parameter regimes.