数据驱动的猜测和粘合不稳定的周期轨道
Pierre Beck1, Jeremy P Parker2, Tobias M Schneider1
1École Polytechnique Fédérale de Lausanne, Emergent Complexity in Physical Systems Laboratory (ECPS), 1015 Lausanne, Switzerland.
Physical review. E
|September 16, 2025
概括
在时空混乱中寻找不稳定的周期轨道 (UPOs) 是一个挑战. 这项研究引入了一种基于数据的方法,使用自动编码器生成初始猜测,显著改善了UPO发现.
科学领域:
- * 动态系统理论
- * 计算物理 计算物理
- * 流体动力学和流动力学
背景情况:
- *不稳定的周期轨道 (UPOs) 是理解时空混乱和流的基础.
- * 寻找UPO的传统方法依赖于生成循环融合算法的初始猜测,这在计算上要求很高,并且通常仅限于更简单的轨道.
- *流体流动状态空间的高维度使得构建合适的初始猜测变得困难.
研究的目的:
- * 开发一种新的,数据驱动的方法,用于生成有效的循环融合算法的初始猜测.
- * 为了利用UPO发现的复杂动态的低维表示.
- * 提高在混乱系统中寻找UPO的效率和适用性.
主要方法:
- * 使用自动编码器来学习一维的Kuramoto-Sivashinsky方程的低维隐藏空间表示.
- * 在潜空间中使用正确直角分解 (POD) 模式与随机周期系数构建了初始猜测 (循环).
- * 将这些潜伏空间循环解码回归到物理空间,以便使用变量收算法.
主要成果:
- * 自动编码器成功捕获了系统的低维混乱吸引器.
- * 潜伏空间中生成的循环作为有效的初始猜测,使UPO能够快速融合.
- * 潜伏空间中的"粘合"程序成功地为更长的UPO生成了猜测,暗示了一个UPO层次结构.
结论:
- * 拟议的数据驱动方法显著提高了在混乱系统中找到UPO的能力.
- * 低维潜空间方法为生成初始猜测的传统方法提供了强大的替代方案.
- *这些发现表明UPO的层次结构,更长的轨道影子序列较短的轨道.
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