arXiv:2412.12036cs.LGcs.RO2024-12中稿 · the 34th Mediterra…被引 1

让机器自动学出非线性系统的动态规律,无需人工设计公式库。

LeARN: Learnable and Adaptive Representations for Nonlinear Dynamics in System Identification

  • 用可学习的神经网络自动构建系统描述所需的函数库,替代人工设计。
  • 在神经飞虫数据集上表现接近经典SINDy方法,且能适应噪声变化。
  • 适合对复杂系统建模但缺乏领域知识的研究者使用。

系统识别是通过观测输入输出数据推导动态系统数学模型的过程。随着基于学习的方法兴起,该领域迎来范式转变。在非线性动态系统数据驱动发现中,稀疏非线性动力学识别(SINDy)成为突破性方法,将复杂行为归纳为基函数的可解释线性组合。然而,SINDy依赖领域专家构建基函数库,限制了其适应性和通用性。本文提出LeARN框架,通过直接从数据中学习基函数库,摆脱对先验知识的依赖。为提升在不同噪声条件下对动态演化模式的适应能力,引入轻量级深度神经网络结合元学习,动态优化基函数。在Neural Fly数据集上的实验验证了该框架的鲁棒性与泛化能力。尽管结构简单,其动态误差表现可媲美SINDy。本工作推动了动态系统自主发现的发展,使机器学习能在无需大量领域干预的情况下揭示复杂系统的内在规律。

原文摘要 · Abstract (English)

System identification, the process of deriving mathematical models of dynamical systems from observed input-output data, has undergone a paradigm shift with the advent of learning-based methods. Addressing the intricate challenges of data-driven discovery in nonlinear dynamical systems, these methods have garnered significant attention. Among them, Sparse Identification of Nonlinear Dynamics (SINDy) has emerged as a transformative approach, distilling complex dynamical behaviors into interpretable linear combinations of basis functions. However, SINDy's reliance on domain-specific expertise to construct its foundational 'library' of basis functions limits its adaptability and universality. In this work, we introduce a nonlinear system identification framework LeARN that transcends the need for prior domain knowledge by learning the library of basis functions directly from data. To enhance adaptability to evolving system dynamics under varying noise conditions, we employ a novel meta-learning-based system identification approach that utilizes a light-weight Deep Neural Network (DNN) to dynamically refine these basis functions. This not only captures intricate system behaviors but also adapts effectively to new dynamical regimes. We validate our framework on the Neural Fly dataset, showcasing its robust adaptation and generalization capabilities. Despite its simplicity, our LeARN achieves competitive dynamical error performance to SINDy. This work presents a step towards autonomous discovery of dynamical systems, paving the way for a future where machine learning uncovers the governing principles of complex systems without requiring extensive domain-specific interventions.

系统识别元学习非线性动力学

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