# Equation Discovery for Nonlinear System Identification

arXiv: https://arxiv.org/abs/1907.00821 · HTML: https://mlsanity.com/paper/1907.00821/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Jul 2019.

## Built on by (most cited first, 7 of 7)

- [Discovering Causal Relations and Equations from Data](https://mlsanity.com/paper/2305.13341/) (2023)
- [Artificial intelligence to advance Earth observation: : A review of models, recent trends, and pathways forward](https://mlsanity.com/paper/2305.08413/) (2023)
- [Predicting Ordinary Differential Equations with Transformers](https://mlsanity.com/paper/2307.12617/) (2023)
- [Known Operator Learning and Hybrid Machine Learning in Medical Imaging -- A Review of the Past, the Present, and the Future](https://mlsanity.com/paper/2108.04543/) (2021)
- [Efficient Generator of Mathematical Expressions for Symbolic Regression](https://mlsanity.com/paper/2302.09893/) (2023)
- [Approximating the universal thermal climate index using sparse regression with orthogonal polynomials](https://mlsanity.com/paper/2508.11307/) (2025)
- [Automated Mathematical Equation Structure Discovery for Visual Analysis](https://mlsanity.com/paper/2104.08633/) (2021)

## Abstract (arXiv)

Equation discovery methods enable modelers to combine domain-specific knowledge and system identification to construct models most suitable for a selected modeling task. The method described and evaluated in this paper can be used as a nonlinear system identification method for gray-box modeling. It consists of two interlaced parts of modeling that are computer-aided. The first performs computer-aided identification of a model structure composed of elements selected from user-specified domain-specific modeling knowledge, while the second part performs parameter estimation. In this paper, recent developments of the equation discovery method called process-based modeling, suited for nonlinear system identification, are elaborated and illustrated on two continuous-time case studies. The first case study illustrates the use of the process-based modeling on synthetic data while the second case-study evaluates on measured data for a standard system-identification benchmark. The experimental results clearly demonstrate the ability of process-based modeling to reconstruct both model structure and parameters from measured data.