Approximating an artificial viscosity operator with neural networks in a shock-capturing scheme

An alternative method for computing artificial viscosity (AV) for shock-capturing is proposed and evaluated on a collection of test problems where shock or discontinuities are present. An artificial neural network (NN) is trained and applied on shock-dominated numerical test problems and used as a means of approximating the AV operator. We present a method to formulate an artificial neural network that predicts artificial viscosity (NN-AV) values using simulation data as the input parameters. This NN-AV is then used to numerically diffuse the shocks in the simulation and the results are compared using the standard AV operator. The artificial neural network is created using standard practices and the TensorFlow library through the collection and training of an input dataset from canonical shock-dominated problems. A simple proof of concept of the NN-AV framework is demonstrated on the viscous Burgers' equation. The model is extended to the Euler equations in both one- and two-dimensions. The accuracy of this trained model is then assessed on other test problems. The accuracy of the results relative to the standard AV operator is evaluated and summarized for all test problems. The order of accuracy for smooth problems and the potential runtime savings from using this new model are discussed.