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.

翻译：从含噪声的高维观测数据中识别潜在动力系统，是表征学习、系统辨识和科学发现交叉领域中的一个核心问题。我们提出DYSCO——一种多视图时间对比学习算法，该算法通过利用同一底层过程的多个独立含噪视图来分离信号与噪声，从而从这些观测数据中联合恢复潜在轨迹及其控制动力学。通过将动力学参数化为结构化函数基，我们的框架进一步能够在仿射规范内对控制方程进行符号恢复。我们提供了可达仿射不确定性下强辨识性的理论保证，将先前的可辨识性结果扩展至含噪非线性观测的现实场景。实验表明，在高斯和泊松观测噪声（后者尤其与神经记录相关）下，我们的方法能在多种动力学模态（如混沌、振荡和亚稳态）中准确恢复潜在轨迹和流场。