提出能量守恒的神经网络模型，提升大涡模拟长期稳定性
Energy-Conserving Neural Network Closure Model for Long-Time Accurate and Stable LES
- 设计反对称神经结构，强制保持质量、动量和能量守恒
- 在多尺度粗化下均稳定运行，但略增耗散
- 优于传统模型，适合长期湍流模拟场景
基于机器学习的大涡模拟（LES）闭包模型虽能捕捉复杂湍流行为，但常出现数值不稳定与物理不一致问题。本文提出一种新型反对称神经架构作为闭包模型，在保证质量、动量和能量守恒的同时实现稳定。该方法采用离散化方案确保守恒律，并引入面平均滤波器维持粗粒化速度场的质量守恒。在衰减湍流与柯莫戈罗夫流动测试中，对比了多种数据驱动闭包模型（包括无约束卷积神经网络）及物理基础的Smagorinsky模型。结果显示，无约束机器学习模型在不同粗化因子下均出现数值发散；而本模型在所有测试中保持稳定，尽管有轻微额外耗散。即便如此，其在未见场景中仍优于Smagorinsky模型。结果表明，结构保持型机器学习闭包具有实现可靠长期大涡模拟的潜力。
原文摘要 · Abstract (English)
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.
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