PARAMOUNT

Parallel Modal Analysis of Large Datasets

PARAMOUNT is a lightweight Python toolkit for computing Proper Orthogonal Decomposition (POD) and Dynamic Mode Decomposition (DMD) on large numerical and experimental datasets. It leverages parallel processing to analyze large amounts of data efficiently.

Overview

• Distributed Processing: Ideal for multi-core parallel processing of large data.
• Methodology: A brief video introduction to the theory is available here.

Proper Orthogonal Decomposition (POD)

• Perform distributed computation of POD to extract dominant spatial patterns.
• Accompanying research paper:

Alireza Ghasemi, et al. "Combustion Dynamics Analysis of a Pressurized Airblast Swirl Burner using Proper Orthogonal Decomposition." International Journal of Spray and Combustion Dynamics, 2023. DOI:10.1177/17568277231207252

Dynamic Mode Decomposition (DMD)

• Compute DMD modes, eigenvalues, and generate future state predictions.
• Multi-resolution DMD (MRDMD) to analyze data across various temporal scales.
• Accompanying research paper:

Alireza Ghasemi, Jim B.W. Kok. "Exploring Liquid Fuel Combustion Dynamics in a Swirl Burner using Dynamic Mode Decomposition." Engineering Applications of Computational Fluid Mechanics, 2025. DOI:10.1080/19942060.2025.2557009

Visualization

• Easily visualize POD/DMD modes and coefficients using Matplotlib.
• 3D data can be visualized interactively with Plotly.

Using PARAMOUNT

1. Installation

   pip install -r requirements.txt

2. Data Preparation

   • PARAMOUNT works well with CSV datasets and can convert them to Parquet for better performance.
   • The domain coordinates x/y/z.pkl are inferred based on input CSV data.
   • Specify variables of interest and convert to Parquet. See csv_example for details.

   # Convert your data into parquet format
   pod = POD()
   variables = POD.get_folderlist(...)
   pod.csv_to_parquet(...)

3. Analysis (POD / DMD / MRDMD)

   • Vertex distance dist may be set to mask out external regions within the domain bounding box.
   • Other parameters such as timestep dt and maximum analysis frequency freq_max can be specified.
   • For POD: use the POD class to compute SVD from Parquet datasets. Results (U, S, V) are stored. See svd_example.

   pod.svd_save_usv(...)

   • For DMD: use the DMD class to compute dynamic modes and eigenvalues. See dmd_example.

   dmd = DMD()
   dmd.save_Atilde(...)
   dmd.save_modes(...)
   dmd.save_prediction(...)

   • For MRDMD: use MRDMD utilities. See mrdmd_example.

   dmd.multires(...)
   dmd.multires_predict(...)

4. Visualization

   • Visualization parameters can be customized.

   pod.set_time(dt)
   pod.set_viz_params(dpi=600, linewidth=0.85, color="black", cmap="seismic")

   • 2D visualization methods for each analysis are included in the provided sample scripts.
   • Interactive 3D visualization of results can be performed similar to the provided 3D_viz_example.ipynb.

Proposed Project Folder Structure

This is a sample project structure for using the PARAMOUNT library to perform POD and DMD analysis.

Project
├── myproject.py
├── .data
│   ├── variable_1/
│   │   └── *.parquet
│   ├── variable_2/
│   │   └── *.parquet
│   ├── x.pkl
│   └── y.pkl
├── .usv
│   ├── variable_1/
│   │   ├── s.pkl
│   │   ├── u/*.parquet
│   │   └── v/*.parquet
│   └── variable_2/
│       ├── s.pkl
│       ├── u/*.parquet
│       └── v/*.parquet
├── .dmd
│   ├── variable_1/
│   │   ├── Atilde.pkl
│   │   ├── b.pkl
│   │   ├── lambda.pkl
│   │   ├── modes_imag/*.parquet
│   │   ├── modes_real/*.parquet
│   │   └── prediction/*.parquet
│   └── variable_2/ ...
├── .mrdmd
│   └── variable_1/levels/...
├── .viz
│   └── variable_1/results.png
└── src
    ├── PARAMOUNT_BASE.py
    ├── PARAMOUNT_POD.py
    ├── PARAMOUNT_DMD.py
    └── utils.py

Notes and Acknowledgements

If you use PARAMOUNT in published work, please cite the relevant associated paper.
This toolkit is developed by Alireza Ghasemi at University of Twente under the MAGISTER project.