Energy-Conserving Neural Network Closure Model for Long-Time Accurate and Stable LES
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| Format: | Preprint |
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2025
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| _version_ | 1866915649852276736 |
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| author | van Gastelen, Toby Edeling, Wouter Sanderse, Benjamin |
| author_facet | van Gastelen, Toby Edeling, Wouter Sanderse, Benjamin |
| contents | Machine learning-based closure models for LES have shown promise in capturing complex turbulence dynamics but often suffer from instabilities and physical inconsistencies. In this work, we develop a novel skew-symmetric neural architecture as closure model that enforces stability while preserving key physical conservation laws. Our approach leverages a discretization that ensures mass, momentum, and energy conservation, along with a face-averaging filter to maintain mass conservation in coarse-grained velocity fields. We compare our model against several conventional data-driven closures (including unconstrained convolutional neural networks), and the physics-based Smagorinsky model. Performance is evaluated on decaying turbulence and Kolmogorov flow for multiple coarse-graining factors. In these test cases we observe that unconstrained machine learning models suffer from numerical instabilities. In contrast, our skew-symmetric model remains stable across all tests, though at the cost of increased dissipation. Despite this trade-off, we demonstrate that our model still outperforms the Smagorinsky model in unseen scenarios. These findings highlight the potential of structure-preserving machine learning closures for reliable long-time LES. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_05868 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Energy-Conserving Neural Network Closure Model for Long-Time Accurate and Stable LES van Gastelen, Toby Edeling, Wouter Sanderse, Benjamin Machine Learning Numerical Analysis 65Mxx Machine learning-based closure models for LES have shown promise in capturing complex turbulence dynamics but often suffer from instabilities and physical inconsistencies. In this work, we develop a novel skew-symmetric neural architecture as closure model that enforces stability while preserving key physical conservation laws. Our approach leverages a discretization that ensures mass, momentum, and energy conservation, along with a face-averaging filter to maintain mass conservation in coarse-grained velocity fields. We compare our model against several conventional data-driven closures (including unconstrained convolutional neural networks), and the physics-based Smagorinsky model. Performance is evaluated on decaying turbulence and Kolmogorov flow for multiple coarse-graining factors. In these test cases we observe that unconstrained machine learning models suffer from numerical instabilities. In contrast, our skew-symmetric model remains stable across all tests, though at the cost of increased dissipation. Despite this trade-off, we demonstrate that our model still outperforms the Smagorinsky model in unseen scenarios. These findings highlight the potential of structure-preserving machine learning closures for reliable long-time LES. |
| title | Energy-Conserving Neural Network Closure Model for Long-Time Accurate and Stable LES |
| topic | Machine Learning Numerical Analysis 65Mxx |
| url | https://arxiv.org/abs/2504.05868 |