论文标题
能量一致的模型减少
Energetically Consistent Model Reduction for Metriplectic Systems
论文作者
论文摘要
Metripercic形式主义对于描述保存能量并产生熵的完整动力系统很有用。这给减少模型带来了挑战，因为消除高频信息通常不会保留控制系统长期稳定性的元学结构。基于适当的正交分解，制定了可证明的收敛性元截止阶层模型，该模型可以保证维持能量保护和熵形成所需的代数结构。基准问题的数值结果表明，所提出的方法非常稳定，导致长期尺度上的精度提高，而成本比幼稚的方法适度增加。
The metriplectic formalism is useful for describing complete dynamical systems which conserve energy and produce entropy. This creates challenges for model reduction, as the elimination of high-frequency information will generally not preserve the metriplectic structure which governs long-term stability of the system. Based on proper orthogonal decomposition, a provably convergent metriplectic reduced-order model is formulated which is guaranteed to maintain the algebraic structure necessary for energy conservation and entropy formation. Numerical results on benchmark problems show that the proposed method is remarkably stable, leading to improved accuracy over long time scales at a moderate increase in cost over naive methods.
