1. Entropy stable conservative flux form neural networks
- Author
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Liu, Lizuo, Li, Tongtong, Gelb, Anne, and Lee, Yoonsang
- Subjects
Mathematics - Numerical Analysis ,Computer Science - Machine Learning ,65M08, 68T07, 65M22, 65M32, 65D25 - Abstract
We propose an entropy-stable conservative flux form neural network (CFN) that integrates classical numerical conservation laws into a data-driven framework using the entropy-stable, second-order, and non-oscillatory Kurganov-Tadmor (KT) scheme. The proposed entropy-stable CFN uses slope limiting as a denoising mechanism, ensuring accurate predictions in both noisy and sparse observation environments, as well as in both smooth and discontinuous regions. Numerical experiments demonstrate that the entropy-stable CFN achieves both stability and conservation while maintaining accuracy over extended time domains. Furthermore, it successfully predicts shock propagation speeds in long-term simulations, {\it without} oracle knowledge of later-time profiles in the training data., Comment: 27 pages, 18 figures
- Published
- 2024