# Sparse dynamical system identification with simultaneous structural parameters and initial condition estimation

arXiv: https://arxiv.org/abs/2204.10472 · HTML: https://mlsanity.com/paper/2204.10472/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Apr 2022.

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

- [Learning Dynamical Systems from Data: A Simple Cross-Validation Perspective, Part V: Sparse Kernel Flows for 132 Chaotic Dynamical Systems](https://mlsanity.com/paper/2301.10321/) (2023)
- [AI-Lorenz: A physics-data-driven framework for black-box and gray-box identification of chaotic systems with symbolic regression](https://mlsanity.com/paper/2312.14237/) (2023)
- [Data-driven Discovery of Digital Twins in Biomedical Research](https://mlsanity.com/paper/2508.21484/) (2025)
- [Physics-Informed Neural Networks for Biological 2D+t Reaction-Diffusion Systems](https://mlsanity.com/paper/2604.18548/) (2026)
- [Impilict Runge-Kutta based sparse identification of governing equations in biologically motivated systems](https://mlsanity.com/paper/2502.20319/) (2025)
- [Towards explainable decision support using hybrid neural models for logistic terminal automation](https://mlsanity.com/paper/2509.07577/) (2025)
- [Data-Driven Learning of Unknown Nonlinear Differential Equations Using Functional Analysis](https://mlsanity.com/paper/2609.04329/) (2026)

## Abstract (arXiv)

Sparse Identification of Nonlinear Dynamics (SINDy) has been shown to successfully recover governing equations from data; however, this approach assumes the initial condition to be exactly known in advance and is sensitive to noise. In this work we propose an integral SINDy (ISINDy) method to simultaneously identify model structure and parameters of nonlinear ordinary differential equations (ODEs) from noisy time-series observations. First, the states are estimated via penalized spline smoothing and then substituted into the integral-form numerical discretization solver, leading to a pseudo-linear regression. The sequential threshold least squares is performed to extract the fewest active terms from the overdetermined set of candidate features, thereby estimating structural parameters and initial condition simultaneously and meanwhile, making the identified dynamics parsimonious and interpretable. Simulations detail the method's recovery accuracy and robustness to noise. Examples include a logistic equation, Lokta-Volterra system, and Lorenz system.