Learning Numerical Viscosity Using Artificial Neural Regression Network

Numerical diffusion plays an important role in deciding the characteristics of numerical schemes for flow problems containing discontinuities. In this work, we attempt to learn the numerical viscosity of underlying three-point shock-capturing schemes using non-linear regression neural network in a supervised learning paradigm. Details on network architecture, used data type and training are elaborated. Computed results by underlying schemes using exact numerical diffusion and predicted diffusion by trained network are given and compared. These results show that the network gives a good approximation of numerical diffusion and computed solutions are indistinguishable from the solution using exact numerical diffusion.

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