Fast data-driven reduced order models for emulating physics-based flexible mesh coastal-ocean models

Physics-based coastal ocean models provide vital insights into local and regional coastal dynamics but require significant computational resources to solve numerically. In this work, we develop data-driven reduced order models (ROMs) using machine learning techniques to emulate a 2D flexible mesh hydrodynamic model of Øresund, the Straight between Denmark and Sweden, achieving orders of magnitude speedup while retaining good accuracy. This Øresund model has complex spatio-temporal dynamics driven by time-varying boundary conditions. Two different approaches to generate ROMs offline are developed and compared. Our objective is to assess the advantage of generating such models offline to enable real-time analysis in the online setting.

The first approach extracts patterns in space and time using principal component analysis and learn mappings from previous states and boundary conditions to future states using gradient boosting. The second approach employs Dynamic Mode Decomposition with control (DMDc) to account for boundary forcing. The reduced models are trained offline on a part of the available 12 months of 30-minute resolution snapshots of surface elevation, and u- and v-components of the depth-averaged currents. In both cases a very low number O(100) of latent space dimensions are necessary to get accurate results at the order of 2-4 cm RMSE compared to the full high-fidelity model.

The emulators provide state estimates online in seconds rather than hours, enabling new applications like uncertainty quantification, data assimilation and parameter optimization that require fast model evaluations. Further developments could look to condition the ROMs on a wider range of potential boundary forcings for scenario exploration. This demonstrates machine learning's potential for accelerating coastal simulations for real-time decision support and planning systems facing long-term change and uncertainty.