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From Initial Data to Boundary Layers: Neural Networks for Nonlinear Hyperbolic Conservation Laws

Created by
  • Haebom

Author

Igor Ciril, Khalil Haddaoui, Yohann Tendero

Outline

This paper addresses the problem of approximating the entropy solution to the initial-boundary value problem of a nonlinear strictly hyperbolic conservation law using neural networks. We present a general and systematic framework for designing efficient and reliable learning algorithms that combine fast convergence during training with accurate predictions. We evaluate the methodology for solving specific relaxed related problems using a series of one-dimensional scalar test cases. These numerical experiments demonstrate the potential of the methodology developed in this paper and its applicability to more complex industrial scenarios.

Takeaways, Limitations

Takeaways: An efficient and accurate neural network-based methodology for approximating the entropy solution of nonlinear strict hyperbolic conservation laws. Its applicability to complex industrial scenarios is demonstrated.
Limitations: Evaluation is limited to one-dimensional scalar test cases. Generalization and applicability to higher-dimensional and vector problems are required. Verification of generality for various types of nonlinear strictly hyperbolic conservation laws is also required.
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