Efficient forecasting models of coastal currents are required for the predictive control of smart vessels with autonomous or remote operating capabilities. Accurate physics-based numerical models demand computational resources that often are unavailable onboard ships; moreover, internet bandwidth at remote locations might not be sufficient to exchange the large computational files with onshore servers. In this case, light and efficient Data-Driven Models (DDM) may be developed to be used as a surrogate for a physics-based model.Currents and surface elevation are hydrodynamic variables driven by astronomic tide potential, allowing for harmonic analysis and synthesis of otherwise irregular solutions of Navier-Stokes equations. Once numerical solutions are obtained and analysed in the Fourier domain, the identified harmonics (tide constituents) can be used as a dataset to train the DDM. One approach to building a DDM is by utilizing a Convolutional Neural Network (CNN).CNN is mainly applied in image recognition processes, where it learns the spatial features of image matrices of pixels arranged in columns and rows and uses the learned features to predict an output. This approach can be applied to 2D or 3D fields of predominantly tidal-driven coastal currents. This paper extends the CNN framework to approximate and predict coastal hydrodynamic state variables in space and time. The depth-averaged Navier-Stokes equations were used to create the dataset necessary to train the adopted CNN autoencoder architecture.Two methods of CNN model development are explored. The first method assesses CNN’s capabilities for time forward prediction, using 2D time series of hydrodynamic variables. The second method investigates CNN’s parameter (using Manning number) prediction ability using 2D spatial plots formed by the top 20 most energetic tidal constituents that were obtained from the numerical solution. The hyperparameters of the CNN model for both methods were carefully optimized and tuned using the loss function, Root Mean Square Error (RMSE). The coefficient of determination, the relative error of the time series, and its amplitude and phase were used to gauge the performance of the CNN model for both methods at the final testing stage.Once accurate solutions are achieved, the trained DDM is almost instantaneous and uses negligible computational resources as compared to traditional fluid solvers. Therefore, trained DDM can be deployed onboard ships where global forecast information (e.g., from Global Forecast System) can be used to provide an accurate prediction of the current forcing. To generate the instantaneous current predictions for navigation and smart ship control, the global data can be pulled or pushed to the ship before the mission.
Read full abstract