An artificial neural network for detecting discontinuities
Dr. Deep Ray
MCSS, Ecole Polytechnique Fédérale de Lausanne,
Switzerland
| Speaker |
Dr. Deep Ray
MCSS, Ecole Polytechnique Fédérale de Lausanne,
Switzerland
|
|---|---|
| When |
Jan 04, 2018
from 11:00 AM to 12:00 PM |
| Where | LH 006 |
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Abstract: High-order methods, such as discontinuous Galerkin (DG) schemes, have gained great popularity in solving hyperbolic systems of conservation laws. However, such methods need to be carefully treated near discontinuities to avoid Gibbs oscillations. In the context of DG methods, this issue can be resolved by i) identifying the troubled-cells in the mesh which contain discontinuities, and ii) suitably limiting the numerical solution in these cells to suppress spurious oscillations. The classical minmod-type TVB limiter is capable of correctly identifying troubled cells, provided its problem-dependent parameter M is chosen appropriately. In general, however, it is difficult to estimate M a priori.
With the objective of constructing a universal troubled-cell indicator that can be used for general conservation laws, we propose a new approach to detect discontinuities using artificial neural networks (ANNs). In particular, a multilayer perceptron (MLP) is constructed, which is trained offline using a supervised learning strategy, and thereafter used as a black-box to identify troubled-cells. The advantage of the proposed ANN method is that it is parameter-free, non-intrusive and can easily be integrated into existing code frameworks. Several numerical results are presented to demonstrate the robustness of the MLP indicator in the framework of Runge-Kutta DG schemes. This work was done jointly with Jan S. Hesthaven.