Dynamic Mode Decomposition for Parametric Fluid Flow Modeling

Spectrally‑Consistent Interpolation via Mode‑Realigned Pointwise Interpolation (MRPWI)

This repository accompanies the research work:

Parametric Dynamic Mode Decomposition for Parametric Fluid Flow Modeling

It provides a complete, reproducible workflow for constructing parametric reduced‑order models (PROMs) using Dynamic Mode Decomposition (DMD). The focus is on:

• Spectrally consistent preprocessing of DMD modes
• Mode‑Realigned Pointwise Interpolation (MRPWI)
• Lagrange interpolation of eigenvalues
• Interpolation of initial conditions ($x_0$)
• Evaluation against PyDMD’s ParametricDMD implementation

The repository includes tools for both laminar cylinder flow and transonic shock buffet analysis.

---

MRPWI_algorithm/

Core algorithms for parametric DMD:

• mode_eigs_prep.py — mode ranking, conjugate‑pair detection, phase alignment
• lagrange_interp.py — Lagrange interpolation of aligned modes, eigenvalues, and x₀

These scripts form the backbone of the MRPWI PROM pipeline.

---

notebooks/

Interactive Jupyter notebooks demonstrating:

• Cylinder flow PROM construction
• PyDMD’s ParametricDMD used as the baseline comparison model
• Preprocessing, alignment, and interpolation of spectral data
• MRPWI evaluation at unseen parameters
• Flow reconstruction, forecasting, and error analysis

This folder contains the full implementation of the evaluation workflow.

---

snapshot_loader/

Utilities for loading CFD data:

• Masked field extraction
• Coordinate and cell‑area loading
• Snapshot matrix construction
• loader_buffet.py for transonic buffet datasets
• Cylinder loader for laminar wake analysis

---

Test Cases

Example CFD setups and data structures used for:

• 2D-Cylinder flow
• Transonic buffet flow

These cases allow users to reproduce the results shown in the notebooks.

---

Methodological Basis

This work builds on and extends the interpolation methodology introduced in:

L. Du, S. Zhang, R. Zhang, S. Zhang
Interpolation‑based parametric reduced‑order models with dynamic mode decomposition
Eastern Institute for Advanced Study / Shanghai Jiao Tong University (2024)

The implementation includes:

• FlowTorch's integral contribution based mode ranking
• Conjugate‑pair reordering
• Phase alignment of modes across parameters
• MRPWI for pointwise interpolation of complex DMD modes
• Lagrange interpolation of eigenvalues
• Interpolation of initial conditions (extension beyond the original paper)

---

Dependencies

• PyDMD ParametricDMD

  • References:
    Demo, N., Tezzele, M., & Rozza, G. (2018). PyDMD: Python Dynamic Mode Decomposition.
    Journal of Open Source Software, 3(22), 530.
    DOI: https://doi.org/10.21105/joss.00530

    Ichinaga, D., Andreuzzi, F., Demo, N., Tezzele, M., Lapo, E., Rozza, G., Brunton, S. L., & Kutz, J. N. (2024).
    PyDMD: A Python Package for Robust Dynamic Mode Decomposition.
    Journal of Machine Learning Research.
    DOI: https://www.jmlr.org/papers/v25/23-0872.html
    arXiv: https://arxiv.org/abs/2307.07862

• FlowTorch DMD

  • Reference:
    Weiner, A., & Semaan, R. (2021). flowTorch – a Python library for analysis and reduced‑order modeling of fluid flows.
    Journal of Open Source Software, 6(68), 3860.
    https://doi.org/10.21105/joss.03860
    Repository: https://github.com/AndreWeiner/flowtorch

• Cylinder case data

  • Based on the open‑source CFD teaching repository:
    https://github.com/AndreWeiner/ml-cfd-lecture

• Transonic buffet case

  • Based on the open‑source buffet setup:
    https://github.com/JanisGeise/buffet_oat15

• NumPy, SciPy, scikit‑learn

• Matplotlib, Seaborn

• OpenFOAM (for CFD data generation)

---

Reproducibility

The workflow is designed to be:

• Deterministic
• Reproducible
• Modular
• Solver‑agnostic

---