Towards a general stabilisation method for conservation laws using a multilayer Perceptron neural network: 1D scalar and system of equations
Han Veiga, Maria, ; Abgrall, Remi
HAL, hal-01856358 / Harvested from HAL
In this work we explore the idea of a parameter free stabilisation method for hyperbolic conservation laws. It is well known that for discontinuous solutions, non-physical oscillations will develop around the discontinuity. There are different methods to control these oscillations, namely, adding a viscosity term to the partial differential equation or using limiters to modify the solution. In this work we show how to use a neural network to identify cells which are in need of stabilisation, which is parameter free and constructed to be independent of the underlying discretization scheme. We show the performance of this trouble cell indicator for a DG scheme for scalar (linear advection) and systems of equations (Euler equations) in one dimension.
Publié le : 2018-06-11
Classification:  limiters,  computing methods,  neural networks,  [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA]
@article{hal-01856358,
     author = {Han Veiga, Maria,  and Abgrall, Remi},
     title = {Towards a general stabilisation method for conservation laws using a multilayer Perceptron neural network: 1D scalar and system of equations},
     journal = {HAL},
     volume = {2018},
     number = {0},
     year = {2018},
     language = {en},
     url = {http://dml.mathdoc.fr/item/hal-01856358}
}
Han Veiga, Maria, ; Abgrall, Remi. Towards a general stabilisation method for conservation laws using a multilayer Perceptron neural network: 1D scalar and system of equations. HAL, Tome 2018 (2018) no. 0, . http://gdmltest.u-ga.fr/item/hal-01856358/