用神经网络精准模拟小尺度效应，提升粗粒度方程的物理准确性。
Subgrid-Scale Parameterization in Burgers' Equation Using Structure-Preserving Neural Networks and Entropy Variables
- 分拆为守恒通量和涡粘性两部分，用结构保持网络学习小尺度通量。
- 还原了全尺度系统的能量谱与时空相关性，精度高。
- 训练外参数也有效，适合实际复杂系统建模。
我们提出一种机器学习方法，用于构建偏微分方程粗粒度模拟中的亚网格尺度（SGS）参数化。通过使用结构保持神经网络和熵变量，学习勃格斯方程粗粒度模拟中的亚网格通量。特别地，采用解耦神经网络架构，将亚网格修正明确分为两个独立部分：守恒通量势网络与涡粘性网络。我们证明该降阶框架保持了高物理保真度，准确再现了全尺度系统的能量谱、空间与时间相关函数及动力学特征。此外，我们的方法在训练范围外的参数下仍具鲁棒性，具备广泛应用潜力。
原文摘要 · Abstract (English)
We present a machine learning approach for developing subgrid-scale (SGS) parametrizations in coarse simulations of partial differential equations. We utilize structure-preserving neural networks and entropy variables to learn subgrid fluxes in coarse simulations of the Burgers' equation. In particular, we employ a decoupled neural network architecture explicitly separating the subgrid corrections into two distinct components: a conservative Flux Potential network and an Eddy Viscosity network. We demonstrate that this reduced-order framework maintains high physical fidelity, accurately reproducing the energy spectrum, spatial and temporal correlation functions, and dynamical characteristics of the full-scale system. Furthermore, we show that our approach is robust and applicable to parameters outside the training regime.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。