modular Sparse Identification of Nonlinear Dynamics

mSINDy - modular Sparse Identification of Nonlinear Dynamics is a modular MATLAB framework for data-driven discovery of governing equations in nonlinear dynamical systems based on sparse regression and the Sparse Identification of Nonlinear Dynamics (SINDy) methodology.

Overview
Features
Usage
Documentation
Authors
Citing mSINDy
License
Institutional support
Funding
Contact

Overview

mSINDy was developed to support the identification, reconstruction, and interpretation of nonlinear dynamical systems directly from data, with emphasis on:

Sparse Identification of Nonlinear Dynamics (SINDy)
Sparse regression for equation discovery
Data-driven identification of governing equations
Reduced-order and interpretable dynamical modeling

The framework is designed to bridge theoretical concepts and practical computational workflows, including scenarios involving noisy measurements, nonlinear oscillations, chaotic dynamics, and limited observational data.

This repository accompanies the developments presented in:

A. Cunha Jr, and C. A. Lampe., Data-driven Evolution Equations via Sparse Identification of Nonlinear Dynamics. In: Scientific Machine Learning for Predictive Modeling: Bridging Data-Driven and Physics-Based Approaches in Computational Science and Engineering, edited by A. Cunha Jr, F. P. Santos, F. A. Rochinha, and A. L. G. A. Coutinho, Springer, 2026.

Features

Sparse identification of governing equations from trajectory data
Polynomial, trigonometric, exponential, and logarithmic candidate libraries
Sequential Thresholded Least Squares (STLS) sparse regression
Sparse coefficient selection and model interpretation
Reconstruction and prediction of nonlinear dynamics
Validation using unseen initial conditions
Handling of noisy datasets and derivative estimation
MATLAB implementations for pedagogical and research applications
Reproducible workflows aligned with published studies

Usage

To get started with mSINDy, follow these steps:

Clone the repository:

git clone https://github.com/americocunhajr/mSINDy.git

Navigate to the package directory:
```
cd mSINDy/mSINDy-1.0
```
Run the mSINDy tutorials provided in the corresponding folders

The code includes the following examples:

Linear harmonic oscillator
Duffing oscillator
van der Pol oscillator
Rossler chaotic system
Noise sensitivity and weak-form sparse identification

Documentation

The routines in mSINDy are well-commented to explain their functionality. Each routine includes a description of its purpose, along with its inputs and outputs. Detailed documentation can be found within the code comments.

Authors

Americo Cunha Jr
Cesar Augusto Lampe

Citing mSINDy

If you use mSINDy in your research, please cite the following publication:

A. Cunha Jr, and C. A. Lampe., Data-driven Evolution Equations via Sparse Identification of Nonlinear Dynamics. In: Scientific Machine Learning for Predictive Modeling: Bridging Data-Driven and Physics-Based Approaches in Computational Science and Engineering, edited by A. Cunha Jr, F. P. Santos, F. A. Rochinha, and A. L. G. A. Coutinho, Springer, 2026.

@incollection{mSINDy2026,
  author    = {A. Cunha Jr and C. A. Lampe},
  title     = {Data-driven Evolution Equations via Sparse Identification of Nonlinear Dynamics},
  booktitle = {Scientific Machine Learning for Predictive Modeling: Bridging Data-Driven and Physics-Based Approaches in Computational Science and Engineering},
  editor    = {Americo Cunha Jr and F. P. Santos and F. A. Rochinha and A. L. G . A. Coutinho},
  publisher = {Springer},
  year      = {2026},
  address   = {Cham},
  url       = {https://sindycode.org},
}

License

mSINDy is released under the MIT license. See the LICENSE file for details. All new contributions must be made under the MIT license.