Entropy stable conservative flux form neural networks

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2411.01746v1.pdf (1.56 MB)

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https://link.springer.com/article/10.1007/s10915-026-03210-1

Permanent Link

https://doi.org/10.1007/s10915-026-03210-1
 http://hdl.handle.net/11603/37061

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UMBC Faculty Collection
UMBC Mathematics and Statistics Department

Author/Creator

Author/Creator ORCID

https://orcid.org/0000-0002-7664-4764

Date

2026-02-18

Type of Work

journal articles
preprints
Text

Department

Program

Citation of Original Publication

Liu, Lizuo, Tongtong Li, Anne Gelb, and Yoonsang Lee. “Entropy Stable Conservative Flux Form Neural Networks.” Journal of Scientific Computing 107, no. 1 (2026): 3. https://doi.org/10.1007/s10915-026-03210-1.

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Subjects

Computer Science - Numerical Analysis
Computer Science - Machine Learning
Mathematics - Numerical Analysis

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.