Simulating Anomalous Dynamics By Adaptive Method Based On Neuron Network

In the case of finite computational grid,stable and accurate approximation of discontinuous solution,such as oscillatory solution,is a very challenging task.When checking oscillatory or strongly discontinuous solutions,it is usually via a prior irregularly cell indicator.Here irregularly cell means the one with bad properties of solutions.The quality and computational expense of solutions of such cases largely depend on their recognition ability of irregularly cell.In order to avoid Gibbs oscillation and to obtain stable and accurate solutions,it usually needs parameter adjustment and indicator setting modulation based on experience to discrete solutions at hands.In the present paper,we devote ourself to develop a strong,accurate and common irregularly cell indicator,which is suitable for general weighted essentially non-oscillatory WENO scheme with minimum user inputs.We apply the method of deep artificial neural network to detect discontinuous points.In particular,we construct a deep forward feedback artificial neural network,which uses unsupervised backpropagation learning strategy for offline training.This indicator learns from analyzing data via supervised learning strategy,whose inputs consist of numerical solutions of given grid and whose outputs are the existence of oscillation in such grid.We employ deep forward feedback artificial neural network to train indicator.Such indicator can not only recognize irregularly cell indicator,but also be independent on parameters related to the problem.We then use the network after training as the black box indicator,and check their viability in the weighted essentially non-oscillatory framework.