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

arXiv: https://arxiv.org/abs/2412.12036 · HTML: https://mlsanity.com/paper/2412.12036/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 22 references that are in the map.
- First posted on arXiv 16 Dec 2024.

## Builds on (most cited first, 8 of 8)

- [Model-Agnostic Meta-Learning for Fast Adaptation of Deep Networks](https://mlsanity.com/paper/1703.03400/) (2017)
- [Meta-Learning in Neural Networks: A Survey](https://mlsanity.com/paper/2004.05439/) (2020)
- [Generalized Inner Loop Meta-Learning](https://mlsanity.com/paper/1910.01727/) (2019)
- [Neural Lander: Stable Drone Landing Control using Learned Dynamics](https://mlsanity.com/paper/1811.08027/) (2018)
- [Neural-Fly Enables Rapid Learning for Agile Flight in Strong Winds](https://mlsanity.com/paper/2205.06908/) (2022)
- [Adaptive-Control-Oriented Meta-Learning for Nonlinear Systems](https://mlsanity.com/paper/2103.04490/) (2021)
- [Neural-Swarm: Decentralized Close-Proximity Multirotor Control Using Learned Interactions](https://mlsanity.com/paper/2003.02992/) (2020)
- [System Identification via Meta-Learning in Linear Time-Varying Environments](https://mlsanity.com/paper/2010.14664/) (2020)

## Built on by (most cited first, 1 of 1)

- [AC-SINDy: Compositional Sparse Identification of Nonlinear Dynamics](https://mlsanity.com/paper/2604.18889/) (2026)

## Abstract (arXiv)

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.