Spatiotemporal GEIM for ultra-real-time prediction of coupled multi-physics in reactor transients using sparse observations

For complex dynamic systems characterized by multi-physics coupling and transient behavior, achieving fast and accurate prediction of physical fields is not just a computational challenge but a technological necessity to ensure safe operation. To address this, we propose a generalized empirical interpolation method (GEIM)-driven forecasting framework that integrates data assimilation with model order reduction, eliminating the need for explicit predictive operators. The core idea is to construct a low-dimensional approximation space, which can be defined over spatial, temporal, or coupled spatiotemporal domains. Sensor locations are optimally selected to assimilate past observations. For comparison, we also develop a prediction method based on extended dynamic mode decomposition (EDMD), which models nonlinear dynamics via a linear Koopman operator acting on a lifted space of observables. We apply all approaches to both single-physical and multi-physical transient forecasting tasks, where the latter requires predicting multiple fields simultaneously using observations from only one field. Numerical experiments are conducted on two multi-physics problems in nuclear reactors: a 2D transient benchmark and a 3D sustained oscillation problem. Results show that in single-physics forecasting, the GEIM-driven methods achieve high accuracy and long-term predictive stability. In multi-physics forecasting, the spatiotemporal coupling methods demonstrate strong performance even for fields with distinct evolutionary trajectories or spatial distributions. Overall, this GEIM-driven forecasting framework enables fast and accurate transient prediction from sparse observations, making it highly suitable for real-time safety monitoring in complex dynamic systems.