论文标题
使用基于轨迹的优化，近似正常吸引不变的歧管
Approximating normally attracting invariant manifolds using trajectory-based optimization
论文作者
论文摘要
由于相应的动力学微分方程的刚度和高尺寸，对现实反应流的数值模拟是一个重大挑战。基于歧管的模型还原技术通过将整个相空间投射到慢动作的流动性上，从而解决了系统的长期行为。在本文中，我们研究了Lebiedz（2004）的基于轨迹的优化方法，该方法确定了这些流形是适当的熵功能的最小化。与该领域的其他方法类似，该方法基于物理和几何直觉，并在多种模型上进行了测试。本文为其有效性提供了严格的解释，显示了它如何近似通常会吸引轨道。它还概述了该方法如何用于近似于非均匀的近似值，从而吸引了较高维度的不变流形。在整篇文章中，我们在Riemannian歧管上使用无坐标公式。这对于受非线性约束（例如绝热约束）的系统特别有用。
The numerical simulation of realistic reactive flows is a major challenge due to the stiffness and high dimension of the corresponding kinetic differential equations. Manifold-based model reduction techniques address this problem by projecting the full phase space onto manifolds of slow motion, which capture the system's long-term behavior. In this article we study the trajectory-based optimization approach by Lebiedz (2004), which determines these manifolds as minimizers of an appropriate entropy functional. Similar to other methods in this field, this approach is based on physical and geometric intuition and was tested on several models. This article provides a rigorous explanation for its effectiveness, showing how it approximates nonuniformly normally attracting orbits. It also outlines how the method can be utilized to approximate nonuniformly normally attracting invariant manifolds of higher dimension. Throughout the article we use a coordinate-free formulation on a Riemannian manifold. This is especially useful for systems subject to nonlinear constraints, e.g., adiabatic constraints.
