使用结构保持神经网络和熵变量对伯格斯方程进行亚网格尺度参数化
Subgrid-Scale Parameterization in Burgers' Equation Using Structure-Preserving Neural Networks and Entropy Variables
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中文总结 AI 辅助
该研究针对偏微分方程粗粒度模拟中的亚网格尺度参数化问题，利用结构保持神经网络和熵变量，采用解耦神经网络架构，实现了高物理保真度的降阶框架，准确再现系统特性，且方法稳健、适用范围广。
中文摘要 AI 辅助
我们提出了一种机器学习方法，用于在偏微分方程的粗粒度模拟中开发亚网格尺度（SGS）参数化。利用结构保持神经网络和熵变量，在伯格斯方程的粗粒度模拟中学习亚网格通量。采用解耦神经网络架构，将亚网格校正明确分为两个不同组件：保守通量势网络和涡粘性网络。结果表明，该降阶框架保持了高物理保真度，能准确再现全尺度系统的能谱、时空相关函数和动力学特性，且方法稳健，适用于训练范围外的参数。
英文摘要
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.
发表机构
- Dept. of Mathematics, University of Houston（数学系，休斯顿大学）
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