OneScience-Group/PINTO-Kovasznay-Flow

PINTO-Kovasznay

Model Introduction

PINTO-Kovasznay is a two-dimensional steady-flow surrogate based on PINTO, the physics-informed Transformer neural operator developed by the QUEST Lab at the Indian Institute of Science (IISc). It combines spatial coordinates, boundary conditions, and Navier–Stokes constraints to predict the velocity and pressure fields of Kovasznay flow.

Paper: PINTO: Physics-informed transformer neural operator for learning generalized solutions of partial differential equations for any initial and boundary condition

Model Description

PINTO-Kovasznay takes query coordinates, boundary coordinates, and boundary values [u, v, p] as input. Query projection, boundary-position encoding, boundary-value encoding, and multi-head cross-attention combine the boundary conditions before the model predicts two velocity components and pressure. Training combines analytical-solution error, boundary-condition error, and steady incompressible Navier–Stokes residuals.

Intended Uses

Use case	Description
Kovasznay-flow prediction	Predict steady velocity and pressure at different kinematic viscosities.
Steady Navier–Stokes solution	Approximate two-dimensional incompressible steady Navier–Stokes flow.
Boundary-aware modeling	Learn the map from boundary locations and values to the full flow solution through cross-attention.

Usage

1. OneCode

Launch the OneCode AI-for-Science environment

2. Manual Setup

Hardware requirements

• A GPU or DCU is recommended.
• A CPU can run imports, forward passes, and small connectivity checks.
• DCU users must install DTK and use a OneScience Python environment compatible with the cluster.

Download the model repository from Hugging Face

pip install -U huggingface_hub
hf download OneScience-Group/PINTO-Kovasznay-Flow --local-dir ./PINTO-Kovasznay-Flow
cd PINTO-Kovasznay-Flow

Install the runtime environment

DCU environment

# Activate DTK first.
conda create -n onescience311 python=3.11 -y
conda activate onescience311
pip install onescience[cfd-dcu] -i http://mirrors.onescience.ai:3141/pypi/simple/ --trusted-host mirrors.onescience.ai

GPU environment

conda create -n onescience311 python=3.11 -y libstdcxx-ng=12 libgcc-ng=12 gcc_linux-64=12 gxx_linux-64=12
conda activate onescience311
pip install onescience[cfd-gpu] -i http://mirrors.onescience.ai:3141/pypi/simple/ --trusted-host mirrors.onescience.ai

Training data

No external dataset is required. scripts/fake_data.py generates training, boundary, and test samples from the analytical Kovasznay solution. See config/config.yaml for configuration details.

The default data setup uses:

• Domain: (x\in[-0.5,1.0]), (y\in[-0.5,1.5])
• Training viscosities (\nu): 0.05, 1/30, 0.02, and 0.0125
• Interior query points: Latin hypercube sampling
• Boundary points: random samples from all four sides of the rectangular domain
• Inputs: query coordinates, boundary coordinates, and boundary [u, v, p]
• Targets: analytical Kovasznay velocity components (u,v) and pressure (p)

The default script is a minimal smoke-training run: it uses 32 interior points per viscosity, 5 points on each boundary side (20 boundary points in total), and one parameter update. This is an analytically generated reproduction experiment rather than a prepackaged dataset.

Train

python scripts/train.py

The best checkpoint is saved to weight/best_model.pt, and a standard-run checkpoint is included in the same location.

Inference

python scripts/inference.py

Outputs are saved to:

results/metrics.json
results/predictions.npz

Metrics for the included checkpoint:

Metric	Value
relative_l2_u	1.029836654663086
relative_l2_v	1.3754936456680298
relative_l2_p	1.0770763158798218
relative_l2_mean	1.1608022054036458

Evaluation and visualization

python scripts/result.py

The summary is saved to results/summary.json.

OneScience

Platform	OneScience repository	OneSkills repository
Gitee	https://gitee.com/onescience-ai/onescience	https://gitee.com/onescience-ai/oneskills
GitHub	https://github.com/onescience-ai/OneScience	https://github.com/onescience-ai/oneskills

Citation and License

• Paper: PINTO: Physics-informed transformer neural operator for learning generalized solutions of partial differential equations for any initial and boundary condition.
• Upstream implementation: quest-lab-iisc/PINTO.
• The upstream PINTO repository does not currently declare a license. The Hugging Face metadata therefore uses the valid identifier other; obtain the necessary permission before publicly redistributing derived code or weights. The paper and all third-party materials remain subject to their respective terms.