Dynamic Mode Decomposition Engine

DynaMoDE - Dynamic Mode Decomposition Engine is a modular framework for data-driven analysis and reduced-order modeling of dynamical systems based on Dynamic Mode Decomposition (DMD) and Koopman operator theory.

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

Overview

DynaMoDE was developed to support the analysis, reconstruction, and interpretation of complex dynamical systems from data, with emphasis on:

Dynamic Mode Decomposition (DMD)
Koopman operator approximation
Spatiotemporal pattern extraction
Reduced-order modeling from experimental or simulated data

The framework is designed to bridge theoretical concepts and practical applications, including scenarios with noisy, sparse, or low-resolution measurements, such as those encountered in thermal systems and engineering experiments.

This repository accompanies the development presented in:

L. S. Araújo, S. da Silva, A. Cunha Jr., Foundations of Dynamic Mode Decomposition for Data-Driven Modeling. 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.
M. E. P. Silva et al., Characterization of Thermal Systems from Noisy and Low-resolution Measurements Using DMD. 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

Data-driven identification of dynamical systems using DMD
Koopman-based modal decomposition and spectral analysis
Reconstruction and prediction of spatiotemporal fields
Handling of noisy, sparse, and low-resolution datasets
Singular value analysis and rank truncation strategies
MATLAB implementations for pedagogical and research use
Reproducible workflows aligned with published studies

Usage

To get started with DynaMoDE, follow these steps:

Clone the repository:

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

Navigate to the package directory:
```
cd STONEHENGE/DynaMoDE-1.0
```
Run the DMD scripts provided in the corresponding folders

The code includes examples of:

Synthetic benchmark datasets (e.g., Ackley and Rastrigin functions)
Experimental thermal data (sensor-based and image-based)
Reconstruction and truncation analysis

Documentation

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

Authors

Lucas Simon Araújo
Maria Eduarda P. Silva
Fernanda Thais Colombo
Samuel da Silva
Americo Cunha Jr

Citing DynaMoDE

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

L. S. Araújo, S. da Silva, A. Cunha Jr., Foundations of Dynamic Mode Decomposition for Data-Driven Modeling. 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{DynaMoDE2026,
  author    = {L. S. Ara{\'u}jo and S. da Silva and A. Cunha Jr},
  title     = {Dynamic Mode Decomposition for Data-Driven Modeling},
  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},
}

License

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