OPTIMIZING STABILIZATION IN SINGULARLY PER- TURBED PROBLEMS WITH SUPG SCHEME

Sangeeta Yadav, Sangeeta Yadav, Sashikumaar Ganesan

Keywords: Convolutional Neural Network, Singularly Perturbed PDEs, Stabilization Scheme

Abstract:

This paper introduces ConvStabNet, a convolutional neural network that
predicts optimal stabilization parameters for the Streamline Upwind Petrov
Galerkin method (SUPG) stabilization scheme. To enhance the accuracy of
SUPG in solving partial differential equations (PDE) with interior and bound-
ary layers, ConvStabNet incorporates a loss function that combines a strong
residual component and a cross-wind derivative term. ConvStabNet utilizes
a shared parameter scheme, enabling the network to learn the correlations
between cell properties and their respective stabilization parameters while
effectively managing the parameter space. Comparative evaluations against
state-of-the-art neural network solvers based on variational formulations
demonstrate the superior performance of ConvStabNet. The results affirm
ConvStabNet as a promising approach for accurately predicting stabilization
parameters in SUPG, thereby establishing it as an improvement over neural
network-based SUPG solvers

Primary Area: applications to physical sciences (physics, chemistry, biology, etc.)

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Submission Number: 9313