从噪声数据中提取隐藏动力系统的演化方程，实现精准建模。
Extracting Governing Equations from Latent Dynamics via Multi-View Contrastive Learning
- 通过多视角对比学习分离信号与噪声，联合恢复隐状态轨迹与动力学。
- 在高斯和泊松噪声下均能准确还原混沌、振荡等复杂动态系统的流场。
- 可符号化恢复控制方程，适合需要物理可解释性的科学发现场景。
从噪声高维观测中识别隐藏动力系统是表征学习、系统辨识与科学发现交叉领域的核心问题。本文提出DYSCO，一种基于多视角时序对比学习的算法，通过利用同一过程的多个独立噪声视图，联合恢复隐状态轨迹与支配性动力学。通过在结构化函数基上参数化动力学，该框架进一步实现仿射规范下的符号方程恢复。我们提供了强可辨识性的理论保证，将先前结果扩展至真实噪声非线性观测场景。实验表明，在高斯与泊松噪声下，该方法在混沌、振荡、亚稳态等多种动力学范式中均能准确恢复隐轨迹与流场，后者对神经记录尤为关键。
原文摘要 · Abstract (English)
Identifying latent dynamical systems from noisy, high-dimensional measurements is a central problem at the intersection of representation learning, system identification, and scientific discovery. We present DYSCO, a multi-view temporal contrastive learning algorithm that jointly recovers latent trajectories and the governing dynamics from such observations, by leveraging multiple independent noisy views of the same underlying process to disentangle signal from noise. By parameterizing the dynamics in a structured functional basis, our framework further enables symbolic recovery of the governing equations within an affine gauge. We offer theoretical guarantees for strong identification up to an affine indeterminacy, extending prior identifiability results to the realistic setting of noisy nonlinear observations. Empirically, we demonstrate accurate recovery of both latent trajectories and flow fields across a diverse set of dynamical regimes (e.g., chaotic, oscillatory, and metastable) under both Gaussian and Poisson observation noise, the latter being particularly relevant for neural recordings.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。