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 relies on domain-specific expertise to construct its foundational "library" of basis functions, which limits its adaptability and universality. In this work, we introduce a nonlinear system identification framework called 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 uses a lightweight deep neural network (DNN) to dynamically refine these basis functions. This not only captures intricate system behaviors but also adapts seamlessly 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 compared to SINDy. This work presents a step toward the 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.

翻译：系统辨识，即从观测的输入-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的出现，已发生范式转变。这些方法致力于应对非线性动态系统中数据驱动发现的复杂挑战，因而受到广泛关注。其中，非线性动力学稀疏辨识（SINDy）作为一种变革性方法脱颖而出，其将复杂的动态行为提炼为基函数的可解释线性组合。然而，SINDy依赖于领域专业知识来构建其基础的基函数“库”，这限制了其适应性与普适性。本文提出了一种名为LeARN的非线性系统辨识框架，该框架通过直接从数据中学习基函数库，从而超越了对先验领域知识的需求。为提升在变化噪声条件下对演化系统动态的适应性，我们采用了一种基于元学习的新型系统辨识方法，该方法利用轻量级深度神经网络（DNN）动态优化这些基函数。这不仅能够捕捉复杂的系统行为，还能无缝适应新的动态机制。我们在Neural Fly数据集上验证了所提框架，展示了其强大的适应与泛化能力。尽管结构简洁，我们的LeARN在动态误差性能上仍达到了与SINDy相当的水平。这项工作向动态系统的自主发现迈进了一步，为机器学习无需大量领域特定干预即可揭示复杂系统支配原理的未来开辟了道路。