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

TL;DR

LeARN introduces a data-driven, adaptive framework for nonlinear system identification that learns basis functions directly from data and adapts to changing dynamics using meta-learning and neural networks.

Contribution

This work presents LeARN, a novel system identification method that eliminates the need for domain-specific basis functions by learning them from data and adapting dynamically via meta-learning.

Findings

LeARN achieves competitive error performance compared to SINDy.

It demonstrates robust adaptation to evolving system dynamics.

The framework generalizes well on the Neural Fly dataset.

Abstract

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.