A surrogate model for depth-averaged erosion and deposition closures using deep learning

Geophysical mass flows are commonly modelled using depth-averaged (DA) numerical models, which rely on closure relations to account for erosion and deposition. While erosion and deposition are grain scale phenomena, their physics is overlooked due to simplifications required in DA models. In this study, a framework is proposed to transfer the grain-scale physics of erosion and deposition to the continuum scale of DA models. A long short-term memory (LSTM) neural network is coupled with a DA model to incorporate the grain-scale physics of erosion and deposition. As a surrogate model for the closure relation, the LSTM model is trained using computed results from grain-scale Discrete Element Method (DEM) simulations. The surrogate model is evaluated by studying the deposition of an initially flowing granular mass over slope. The effective flow depth h and DA velocity u calculated by the DA-LSTM model are compared with DEM simulation results. The DA-LSTM model is demonstrated to provide more computational efficiency compared to DEM simulations. The newly proposed surrogate model offers a promising approach to calculating more complex closures using deep learning techniques.