PyDMD: A Python Package for Dynamic Mode Decomposition (DMD)

2025-12-18 · Source: Steve Brunton · Field: Technology & Digital — Artificial Intelligence & Machine Learning, Data Science & Analytics · Depth: Intermediate, extended

Summary

The PyDMD Python package provides implementations for Dynamic Mode Decomposition (DMD), a data-driven method for modeling complex, time-varying systems. Developed and maintained by contributors from the University of Washington, PyDMD offers various DMD variants, extensions, optimized algorithms, data preprocessors, and plotting tools. The package helps users analyze time-varying snapshot data to derive mathematical models, particularly when precise governing equations are unknown. The core DMD algorithm decomposes data into spatial modes, temporal dynamics (frequencies), and amplitudes, which together describe the dominant spatio-temporal features. A coding demonstration illustrates using PyDMD's `BOPDMD` model to reconstruct a noisy synthetic dataset comprising two spatio-temporal modes, accurately recovering their underlying frequencies and spatial signatures with a relative error of approximately 5%. PyDMD is modular, similar to scikit-learn, allowing users to define, parameterize, fit models, and visualize results with functions like `plot_summary`.

Key takeaway

For Data Scientists or Machine Learning Engineers working with time-varying observational data where governing equations are elusive, PyDMD offers a robust, scikit-learn-like framework to extract underlying spatio-temporal dynamics. You should consider using `BOPDMD` for noisy datasets, as it effectively identifies dominant modes and their frequencies, enabling accurate data reconstruction and system understanding. Explore PyDMD's tutorials for advanced customization, such as constraining eigenvalue properties for specific dynamic expectations.

Key insights

PyDMD enables data-driven modeling of complex systems by decomposing time-varying data into dominant spatio-temporal modes.

Principles

• DMD assumes linear system dynamics.
• SVD rank parameter guides mode discovery.
• Amplitudes indicate mode importance.

Method

Define a PyDMD model (e.g., `BOPDMD`), parameterize it (e.g., `svd_rank=2`), fit it to snapshot data and time points, then access attributes like `modes`, `dynamics`, `amplitudes`, and `reconstructed_data`.

In practice

• Use `BOPDMD` for noise-robust analysis.
• Install PyDMD from GitHub for latest updates.
• Utilize `plot_summary` for comprehensive visualization.

Topics

• Dynamic Mode Decomposition
• PyDMD Python Package
• Spatio-Temporal Modes
• Data-Driven Modeling
• BOP-DMD Algorithm

Best for: Machine Learning Engineer, Data Scientist, Research Scientist

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Editorial summary, takeaway, and curation by AIssential. Original article published by Steve Brunton.