用自编码器潜空间预测混沌系统稳定性，突破传统方法局限。
Inferring stability properties of chaotic systems on autoencoders' latent spaces
- 将混沌系统压缩至潜空间，通过递归网络推断动力学稳定性。
- 成功从潜空间提取李雅普诺夫指数与协变向量，揭示稳定性质。
- 适合研究高维混沌系统的科研人员，为动力学分析提供新路径。
基于数据驱动的方法可采用分而治之策略：首先使用自编码器将高维数据压缩到潜空间；其次在潜空间中利用循环神经网络推断时间演化。在混沌系统与湍流中，卷积自编码器与回声状态网络（CAE-ESN）已成功实现动态预测，但其对稳定性性质的推断尚不明确。本文证明，CAE-ESN模型能从潜空间中推断出不变的稳定性属性及切空间几何结构，方法基于李雅普诺夫指数与协变李雅普诺夫向量。该研究为在潜空间中推断高维混沌系统的稳定性开辟了新可能。
原文摘要 · Abstract (English)
The data-driven learning of solutions of partial differential equations can be based on a divide-and-conquer strategy. First, the high dimensional data is compressed to a latent space with an autoencoder; and, second, the temporal dynamics are inferred on the latent space with a form of recurrent neural network. In chaotic systems and turbulence, convolutional autoencoders and echo state networks (CAE-ESN) successfully forecast the dynamics, but little is known about whether the stability properties can also be inferred. We show that the CAE-ESN model infers the invariant stability properties and the geometry of the tangent space in the low-dimensional manifold (i.e. the latent space) through Lyapunov exponents and covariant Lyapunov vectors. This work opens up new opportunities for inferring the stability of high-dimensional chaotic systems in latent spaces.
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