Sparse identification of nonlinear dynamics (SINDy) has been widely used to discover the governing equations of a dynamical system from data. It uses sparse regression techniques to identify parsimonious models of unknown systems from a library of candidate functions. Therefore, it relies on the assumption that the dynamics are sparsely represented in the coordinate system used. To address this limitation, one seeks a coordinate transformation that provides reduced coordinates capable of reconstructing the original system. Recently, SINDy autoencoders have extended this idea by combining sparse model discovery with autoencoder architectures to learn simplified latent coordinates together with parsimonious governing equations. A central challenge in this framework is robustness to measurement error. Inspired by noise-separating neural network structures, we incorporate a noise-separation module into the SINDy autoencoder architecture, thereby improving robustness and enabling more reliable identification of noisy dynamical systems. Numerical experiments on the Lorenz system show that the proposed method recovers interpretable latent dynamics and accurately estimates the measurement noise from noisy observations.

翻译：稀疏非线性动力学辨识（SINDy）已被广泛用于从数据中发现动力系统的控制方程。它利用稀疏回归技术从候选函数库中识别未知系统的简约模型。因此，该方法依赖于动力系统在所用坐标系中具有稀疏表示的假设。为克服这一局限，人们寻求一种坐标变换，以提供能够重构原始系统的约化坐标。近年来，SINDy自编码器通过将稀疏模型发现与自编码器架构相结合，在学习简化潜坐标的同时获取简约控制方程，拓展了上述思路。该框架的核心挑战在于对测量误差的鲁棒性。受噪声分离神经网络结构启发，我们在SINDy自编码器架构中融入噪声分离模块，从而提升鲁棒性，实现含噪动力系统的更可靠辨识。在洛伦兹系统上的数值实验表明，所提方法能恢复可解释的潜动力学，并基于含噪观测准确估计测量噪声。