Energy-Conserving Neural Network for Turbulence Closure Modeling: Stability and Structure Preservation

핵심 개념

Neural network architecture ensures stability and energy conservation in turbulence closure modeling.

초록

In the realm of turbulence modeling, machine learning techniques are increasingly utilized to construct closure models that represent the interaction between subgrid scales and resolved scales. The challenge lies in ensuring stability and abidance by physical laws such as conservation of energy, momentum, and mass. To address these issues, a novel approach is introduced that incorporates an additional set of equations to dynamically model the energy of subgrid scales. This method guarantees stability by conserving total energy through a skew-symmetric convolutional neural network architecture. The framework allows for backscatter modeling and extends to dissipative systems like viscous flows. By introducing SGS variables to approximate SGS energy projected onto a coarse grid, the closure model satisfies both momentum and kinetic energy conservation laws. The proposed methodology is applied to Burgers’ equation and Korteweg-de Vries equation in 1D, demonstrating superior stability properties compared to traditional approaches.

통계

Recent approaches gravitate towards machine learning techniques for turbulence modeling.
Stability remains an important issue in machine-learned closure models.
Machine learning approaches have shown promise but struggle with stability and structure preservation.
Convolutional neural networks have been used as viable closure models but face challenges with stability.
Trajectory fitting and reinforcement learning are promising approaches to improve the stability of NN closure models.

인용구

"Machine learning approaches have come forward as viable closure models but struggle with stability."
"Convolutional neural networks have been shown to outperform classical approaches but face challenges with abidance by physical laws."
"Stability remains an important issue along with abidance by physical structure such as mass, momentum, and energy conservation."

핵심 통찰 요약

Energy-Conserving Neural Network for Turbulence Closure Modeling

by Toby van Gas... 게시일 arxiv.org 03-18-2024

https://arxiv.org/pdf/2301.13770.pdf

더 깊은 질문

How can trajectory fitting and reinforcement learning enhance the stability of neural network closure models

Trajectory fitting and reinforcement learning can enhance the stability of neural network closure models by optimizing the model parameters to directly reproduce the solution trajectory rather than just fitting the derivative. This approach ensures that the model accurately captures how well it reproduces the dynamics of the system over time, leading to more stable and accurate predictions. Trajectory fitting uses exact gradients to optimize the weights of the neural network based on how well it reproduces the solution trajectory, ensuring a more accurate and stable closure model. On the other hand, reinforcement learning does not require these gradients, making it suitable for optimizing non-differentiable processes like turbulence closure modeling.

What are the implications of using a skew-symmetric convolutional neural network architecture for turbulence closure modeling

Using a skew-symmetric convolutional neural network architecture for turbulence closure modeling has significant implications for structure preservation and stability. The skew-symmetry in this architecture allows for energy exchange between resolved scales and subgrid scales while maintaining momentum conservation properties. By incorporating this symmetry into the design of neural networks used in turbulence closure modeling, we ensure that energy is conserved in inviscid limits and backscatter phenomena are accurately captured without sacrificing stability. This unique architecture enables better representation of physical principles such as conservation laws within turbulent flow systems.

How does the introduction of SGS variables impact the accuracy and stability of the proposed methodology

The introduction of SGS variables impacts both accuracy and stability in turbulence closure modeling methodology significantly. These variables represent an approximation of subgrid-scale (SGS) energy projected onto a coarse grid, allowing for a more detailed representation of energy distribution within turbulent flows at smaller scales. By including SGS variables in the framework, we improve accuracy by capturing finer details related to SGS content near shocks or areas with high variability. Additionally, incorporating SGS variables enhances stability by providing additional information about energy exchanges between resolved scales and subgrid scales, leading to more robust simulations with reduced numerical instabilities.