Abstract :

The demand for approximation accuracy and convergence behavior of computed solutions restricts the application of deep learning networks in the domain of scientific computing. Moreover, the recipe to create suitable synthetic data which can be used to have a good trained model is also not very clear. This talk will focus on learning third order essentially non-oscillatory (ENO3) and a new weighted ENO3 reconstruction using classification neural networks such that trained models preserve accuracy and non-oscillatory properties of ENO3 and WENO3 schemes. This work elaborated (i) a simple approach to construct trained data sets (ii) that sampling of train data impacts quantitatively as well qualitatively such required properties in the trained models (iii) uses a hybrid approach to use trained models for retaining desired accuracy as well non-oscillatory properties of ENO3 and WENO3 schemes for hyperbolic PDE's. Numerical results are presented to support the hypotheses and performance of learned networks.