Adjoint model based deep learning for efficient pointwise residence time estimation in coastal environments

Residence time is an essential quantitative diagnosis for evaluating water renewal and pollutant retention in coastal environments. However, its computation remains challenging due to the spatial and temporal variability of the coastal flows. Traditional techniques are usually based on simplifying hypotheses that fail to capture the dynamic conditions accurately. We introduce a new deep learning framework that uses a convolutional Long Short-Term Memory network (ConvLSTM) to solve the adjoint advection-diffusion problem that leads to spatially and temporally resolved residence time without the necessity to store extensive hydrodynamic histories. Our approach utilizes high-resolution data generated by solving the shallow water equations using a non-homogeneous Riemann solver (SRNH). We use a data reduction approach to address the substantial computing difficulties posed by full-resolution data. Initially, the ConvLSTM is trained using full data for the initial waiting period of the simulation to establish robust recognition of hydrodynamic models. After that, temporal and spatial resolutions are progressively reduced to preserve the essential characteristics of the model. As a result, the computational cost has been reduced from 48 h using the traditional data storage method to 3 h using the ConvLSTM-trained model. Additionally, the memory required to store the hydrodynamics data has been reduced from 14 TB to 800 MB, demonstrating the efficiency of the proposed method in both computational and memory usage.