DOMAIN DECOMPOSITION FOR ENHANCEMENT OF REDUCED-ORDER MODELS

Decision-support systems for environmental management of coastal areas must account for brine and seawater dynamics. Physics-based models of these phenomena are computationally expensive, which limits their usefulness for decision-making under uncertainty. Data-driven modeling techniques, such as extended dynamic mode decomposition (xDMD), ameliorate these challenges. We demonstrate that xDMD, equipped with a novel domain decomposition component, effectively represents a validated, real-world, coupled nonlinear seawater inundation model. It serves as an efficient surrogate of process-based simulations, capable of accurate reproduction and reconstruction of missing pressure and salinity data in the interpolation regime. It accurately predicts low-rank pressure distributions (repeated dynamics) but struggles to forecast long-term salinity dynamics (cumulative evolution). The addition of domain decomposition improves the robustness and accuracy of xDMD, with the overlapping domain approach outperforming the nonoverlapping one in the projection accuracy. In our experiments, xDMD is 1700 times faster than the process-based model and requires 800 times less storage, while efficiently capturing pressure and salinity dynamics.