发表机构
Chandar Research Lab; Mila – Quebec AI Institute; Université de Montréal; University of Pennsylvania; NVIDIA; Polytechnique Montréal（钱达尔研究实验室; 米拉-魁北克人工智能研究所; 蒙特利尔大学; 宾夕法尼亚大学; 英伟达; 蒙特利尔理工学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究提出稀疏Koopman自编码器（SKAEs），无需标签即可识别多盆系统的局部动力学 regime，其预测性能优于密隐KAEs，且隐支撑可有效识别吸引盆。
AI 中文摘要
Koopman自编码器（KAEs）旨在寻找高维隐表示，其中非线性动力学以线性方式演化。然而，许多有趣的系统具有多个吸引盆，理论和实证研究均表明，在标准假设下，这些多盆系统通常无法接受单一有限维全局Koopman嵌入。我们假设，带有稀疏性诱导目标函数的编码器（该目标函数鼓励少量活跃隐系数）将为Koopman自编码器提供可检查的盆建模原理的隐支撑。我们使用这些在训练中产生稀疏隐的编码器构建稀疏Koopman自编码器（SKAEs），无需盆标签或其他 regime 注释，并在训练后将学习到的隐支撑视为模型生成的 regime 变量。在一系列程序生成的多盆系统和混沌流中，我们表明，与密隐KAEs相比，SKAEs具有更优异的预测性能。我们还进行了机制研究，结果显示，SKAEs产生的隐支撑对于表示质量至关重要，且可用于识别保留的盆内部状态上的盆，而密隐KAEs则会坍缩为无信息的单一类别。这些结果表明，稀疏隐及其对应的支撑是无标签、可解释的 regime 变量，适用于具有多个局部动力学定律的非线性系统的Koopman学习。
英文摘要
Koopman autoencoders (KAEs) seek a higher-dimensional latent representation in which nonlinear dynamics evolve linearly. However, many interesting systems have multiple basins of attraction, and both theoretical and empirical work has shown these multibasin systems cannot generally admit a single finite-dimensional global Koopman embedding under standard assumptions. We posit that encoders with a sparsity-inducing objective encouraging few active latent coefficients will provide latent supports as an inspectable basin-modeling principle for Koopman autoencoders. We use these encoders producing sparse latents in training Sparse Koopman Autoencoders (SKAEs) without basin labels or other regime annotations, and treat the learned latent supports as model-produced regime variables after training. Across a range of procedurally generated multibasin systems and chaotic flows, we show that SKAEs have superior forecasting performance compared to dense-latent KAEs. We also perform a mechanistic study that shows latent supports produced by SKAEs are both essential for the quality of the representation and useful for identifying basins on held-out basin interior states, whereas dense-latent KAEs collapse to an uninformative single family. These results identify sparse latents and their corresponding supports as label-free, interpretable regime variables for Koopman learning in nonlinear systems with multiple local dynamical laws.
