Modular compositional learning improves 1D hydrodynamic lake model performance by merging process-based modeling with deep learning

Hybrid Knowledge-Guided Machine Learning (KGML) models, which are deep learning models that utilize scientific theory and process-based model simulations, have shown improved performance over their process-based counterparts for the simulation of water temperature and hydrodynamics. We highlight the modular compositional learning (MCL) methodology as a novel design choice for the development of hybrid KGML models in which the model is decomposed into modular sub-components that can be process-based models and/or deep learning models. We develop a hybrid MCL model that integrates a deep learning model into a modularized, process-based model. To achieve this, we first train individual deep learning models with the output of the process-based models. In a second step, we fine-tune one deep learning model with observed field data. In this study, we replaced process-based calculations of vertical diffusive transport with deep learning. Finally, this fine-tuned deep learning model is integrated into the process-based model, creating the hybrid MCL model with improved overall projections for water temperature dynamics compared to the original process-based model. We further compare the performance of the hybrid MCL model with the process-based model and two alternative deep learning models and highlight how the hybrid MCL model has the best performance for projecting water temperature, Schmidt stability, buoyancy frequency, and depths of different isotherms. Modular compositional learning can be applied to existing modularized, process-based model structures to make the projections more robust and improve model performance by letting deep learning estimate uncertain process calculations.