改进的自编码器让复杂系统在有噪声时仍能准确识别动力学方程。
A Robust SINDy Autoencoder for Noisy Dynamical System Identification
- 用带去噪模块的自编码器学习简化坐标，同时发现简洁的动力学方程。
- 在洛伦兹系统上测试，能从含噪声数据中恢复可解释的隐状态和噪声水平。
- 适合做非线性系统建模、含噪声数据下的动态分析的研究者。
稀疏非线性动力学识别（SINDy）广泛用于从数据中发现动力学系统的控制方程，通过稀疏回归从候选函数库中识别出简洁的模型。该方法依赖于系统在所选坐标系中具有稀疏表示的假设。为克服此限制，需寻找一个坐标变换，使新坐标能重建原系统。最近，SINDy自编码器通过结合稀疏建模与自编码器结构，实现隐空间坐标的联合学习与简洁方程的发现。该框架的核心挑战是对测量误差的鲁棒性。受噪声分离神经网络启发，本文在SINDy自编码器中引入噪声分离模块，显著提升对噪声的鲁棒性，实现更可靠的噪声系统建模。在洛伦兹系统的数值实验中，该方法成功恢复了可解释的隐动力学，并准确估计了观测噪声水平。
原文摘要 · Abstract (English)
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.
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