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

Abstract:

The field of system identification—defined as the derivation of mathematical models for dynamical systems using observed input-output data—has experienced a fundamental transformation through the rise of learning-based techniques. These data-driven methods have attracted considerable interest for their ability to tackle the complex challenges inherent in discovering nonlinear dynamical systems. A notable innovation within this domain is Sparse Identification of Nonlinear Dynamics (SINDy), which has revolutionized the field by reducing complex dynamical behaviors into interpretable linear combinations of basis functions. Nevertheless, SINDy’s dependence on domain-specific expertise to manually construct its initial library of basis functions restricts its universality and adaptability.

To overcome these limitations, we propose LeARN, a nonlinear system identification framework that eliminates the need for prior domain knowledge by automatically learning the basis function library directly from data. To further improve adaptability to shifting system dynamics across different noise environments, we integrate a novel meta-learning-based strategy. This approach employs a lightweight Deep Neural Network (DNN) to dynamically refine the basis functions, enabling the model to capture intricate system behaviors and adjust effectively to new dynamical regimes. We demonstrate the efficacy of our framework using the Neural Fly dataset, highlighting its strong generalization and robust adaptation capabilities. Although structurally simple, LeARN delivers dynamical error performance comparable to SINDy. This study marks a significant advance toward the autonomous discovery of dynamical systems, suggesting a future in which machine learning can reveal the governing principles of complex systems without requiring extensive domain-specific intervention.

Source: arXiv Generated at: 2026-06-02 00:00:00 UTC