Entropy stable conservative flux form neural networks
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Abstract (arXiv)
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.
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References · 8
- 2017PDE-Net: Learning PDEs from Datacited by 304
- 2022Continuous PDE Dynamics Forecasting with Implicit Neural Representationscited by 71
- 2020dynoNet: a neural network architecture for learning dynamical systemscited by 28
- 2021Deep Neural Network Modeling of Unknown Partial Differential Equations in Nodal Spacecited by 25
- 2023Flow Map Learning for Unknown Dynamical Systems: Overview, Implementation, and Benchmarkscited by 18
- 2021NeuralPDE: Modelling Dynamical Systems from Datacited by 9
- 2022Recurrent Neural Networks for Dynamical Systems: Applications to Ordinary Differential Equations, Collective Motion, and Hydrological Modelingcited by 9
- 2024Learning WENO for entropy stable schemes to solve conservation lawscited by 1
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