| --- |
| language: |
| - en |
| license: mit |
| arxiv: 2506.08604 |
| task_categories: |
| - other |
| tags: |
| - physics |
| - pde |
| - flow-matching |
| - scientific-machine-learning |
| --- |
| |
| # Physics vs Distributions: Pareto Optimal Flow Matching with Physics Constraints |
|
|
| <div> |
| |
| [](https://arxiv.org/abs/2506.08604) |
| [](https://github.com/tum-pbs/PBFM) |
|
|
| </div> |
|
|
| This repository contains the datasets for the **dynamic stall** and **Kolmogorov flow** cases presented in the paper "[Physics vs Distributions: Pareto Optimal Flow Matching with Physics Constraints](https://huggingface.co/papers/2506.08604)". |
|
|
| ## Dynamic Stall dataset |
| The design space is defined as a four-dimensional hypercube. The design variables are: |
| | Design variable | Symbol | Description | Range | |
| |-------------------------|----------------------------------------|------------------------------------------------------|-------------| |
| | Free-stream Mach number | $ M_{\infty} $ | Ratio of free-stream velocity to speed of sound | 0.3 – 0.5 | |
| | Mean angle of attack | $ \alpha_0 $ | Average angle between chord line and flow direction | 5° – 10° | |
| | Pitching amplitude | $ \alpha_s $ | Maximum angular deviation during pitching motion | 5° – 10° | |
| | Reduced frequency | $ k = \dfrac{\omega c}{2V_{\infty}} $ | Non-dimensional frequency of oscillation | 0.05 – 0.1 | |
|
|
| The hypercube is sampled with **128 points for training** and **16 points for testing**. Each sampled point represents a nominal operating condition. |
|
|
| Each nominal condition is perturbed as follows: |
|
|
| $$ |
| x_{\text{perturbed}} = (1 + \mathcal{N}(0, 0.02)) \cdot x_{\text{nominal}} |
| $$ |
|
|
| where $\mathcal{N}(0, 0.02)$ denotes a Gaussian noise term with zero mean and standard deviation 0.02. |
|
|
| This results in **32 perturbed variations per nominal condition**, yielding a total of: |
|
|
| - $128 \times 32 = 4096$ simulations for training |
| - $16 \times 32 = 512$ simulations for testing |
|
|
| Each simulation that corresponds to a dataset sample has 6 fields of size $128 \times 128$. The fields correspond to: |
| - Absolute pressure |
| - x-wall tangential velocity gradient |
| - y-wall tangential velocity gradient |
| - Temperature |
| - Density |
| - Wall shear stress |
|
|
| Each `hdf5` file contains three arrays: |
| - `fields` with shape `(conditions, samples per condition, fields, x, y)` |
| - `nominal_condition` with shape `(nominal conditions, samples per condition, design variables)` |
| - `real_condition` with shape `(real conditions, samples per condition, design variables)` |
|
|
| ## Kolmogorov flow dataset |
| The Kolmogorov flow problem spans Reynolds numbers |
| in the range $[100, 500]$, using a spatial resolution of $128 \times 128$. The simulations are performed using [TorchFSM](https://zenodo.org/records/15350210). The **training dataset includes 32 different flow conditions**, while the **validation dataset contains 16 conditions**. Each condition has $1\, 024$ snapshots. |
|
|
| Each simulation that corresponds to a dataset sample has 2 fields of size $128 \times 128$. The fields correspond to: |
| - x-velocity |
| - y-velocity |
|
|
| Each `hdf5` file contains two arrays: |
| - `fields` with shape `(conditions, samples per condition, fields, x, y)` |
| - `reynolds` with shape `(reynolds numbers, )` |
|
|
| ## Citation |
|
|
| ```bibtex |
| @inproceedings{pbfm2026, |
| title={Physics vs Distributions: Pareto Optimal Flow Matching with Physics Constraints}, |
| author={Giacomo Baldan and Qiang Liu and Alberto Guardone and Nils Thuerey}, |
| booktitle={The Fourteenth International Conference on Learning Representations}, |
| year={2026}, |
| url={https://openreview.net/forum?id=tAf1KI3d4X} |
| } |
| ``` |
