Enhancing interpretability and generalizability of deep learning-based emulator in three-dimensional lake hydrodynamics using Koopman operator and transfer learning: Demonstrated on the example of lake Zurich

Three-dimensional lake hydrodynamic model is a powerful tool widely used to assess hydrological condition changes of lake. However, its computational cost becomes problematic when forecasting the state of large lakes or using high-resolution simulation in small-to-medium size lakes. One possible solution is to employ a data-driven emulator, such as a deep learning (DL) based emulator, to replace the original model for fast computing. However, existing DL-based emulators are often black-box and data-dependent models, causing poor interpretability and generalizability in practical applications. In this study, a data-driven emulator is established using deep neural network (DNN) to replace the original model for fast computing of three-dimensional lake hydrodynamics. Then, the Koopman operator and transfer learning (TL) are employed to enhance the interpretability and generalizability of the emulator. Finally, the generalizability of DL-based emulators is comprehensively analyzed through linear regression and correlation analysis. These methods are tested against an existing hydrodynamic model of Lake Zurich (Switzerland) whose data was provided by an open-source web-based platform called Meteolakes/Alplakes. According to the results, (1) The DLEDMD offers better interpret-ability than DNN because its Koopman operator reveals the linear structure behind the hydrodynamics; (2) The generalization of the DL-based emulators in three-dimensional lake hydrodynamics are influenced by the similarity between the training and testing data; (3) TL effectively improves the generalizability of the DL-based emulators.