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A deep learning initialized iterative (Int-Deep) method is developed fornumerically solving Navier-Stokes Darcy model. For this purpose, Newtoniterative method is mentioned for solving the relative finite elementdiscretized problem. It is proved that this method converges quadratically withthe convergence rate independent of the finite element mesh size under certainstandard conditions. Later on, a deep learning algorithm is proposed forsolving this nonlinear coupled problem. Following the ideas of an earlier workby Huang, Wang and Yang (2020), an Int-Deep algorithm is constructed for theprevious problem in order to further improve the computational efficiency. Aseries of numerical examples are reported to confirm that the Int-Deepalgorithm converges to the true solution rapidly and is robust with respect tothe physical parameters in the model.

A deep learning initialized iterative method for Navier-Stokes Darcy model