# A kernel-based approach to physics-informed nonlinear system identification

arXiv: https://arxiv.org/abs/2509.07634 · HTML: https://mlsanity.com/paper/2509.07634/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Sep 2025.

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

- [Learning Physical Operators using Neural Operators](https://mlsanity.com/paper/2602.23113/) (2026)

## Abstract (arXiv)

This paper presents a kernel-based framework for physics-informed nonlinear system identification. The key contribution is a structured methodology that extends kernel-based techniques to seamlessly embed partially known physics-based models, improving parameter estimation and overall model accuracy. The proposed method enhances traditional modeling approaches by embedding a parametric model, which provides physical interpretability, with a kernel-based function, which accounts for unmodeled dynamics. The two models' components are identified from the data simultaneously, thereby minimizing a suitable cost that balances the relative importance of the physical and the black-box parts of the model. Additionally, nonlinear state smoothing is employed to address scenarios involving state-space models with not fully measurable states. Numerical simulations on an experimental benchmark system demonstrate the effectiveness of the proposed approach, achieving up to 51% reduction in simulation root mean square error compared to physics-only models and 31% performance improvement over state-of-the-art identification techniques.