Allanatrix/CFD

Navier-Stokes Simulated Flow Dataset for PINNs

Welcome to the Dataset!

Dive into the dynamic world of fluid flow with the Navier-Stokes Simulated Flow Dataset for PINNs! This collection of 10,000 simulated data points captures the essence of fluid dynamics in a 2D channel, tailored specifically for training Physics-Informed Neural Networks (PINNs). With an even split of 5,000 laminar flow and 5,000 turbulent flow points, this dataset is perfect for researchers, data scientists, and students exploring how to model fluid behavior using cutting-edge machine learning techniques. Whether you’re studying smooth laminar flows or chaotic turbulent ones, this dataset offers a compact yet representative resource to power your PINN experiments.

Context

The Navier-Stokes equations are the cornerstone of fluid dynamics, describing how fluids move under forces like pressure and viscosity. Solving these equations is a challenge, especially for turbulent flows, where chaos reigns. Traditional numerical solvers, like direct numerical simulation (DNS), are computationally expensive, but PINNs offer a promising alternative by embedding the equations into neural networks. This dataset, inspired by PINN research (e.g., the paper on PINNs for Navier-Stokes), provides simulated flow data to train models that learn the physics of fluids directly from data and equations. It’s a bridge between computational fluid dynamics and machine learning, ideal for advancing research and education.

Dataset Description

Content

The dataset contains 10,000 rows of simulated flow data in a 2D channel, evenly divided between 5,000 laminar flow and 5,000 turbulent flow points. Each row represents a point in a spatial-temporal grid with the following features:

• x, y: Spatial coordinates in the 2D channel (in meters).
• t: Time coordinate (in seconds).
• u, v: Velocity components in the x- and y-directions (in m/s, non-zero).
• p: Pressure at the point (in Pa).
• u_x, u_y, u_t: Spatial (∂u/∂x, ∂u/∂y) and temporal (∂u/∂t) derivatives of u.
• v_x, v_y, v_t: Spatial (∂v/∂x, ∂v/∂y) and temporal (∂v/∂t) derivatives of v.
• p_x, p_y, p_t: Spatial (∂p/∂x, ∂p/∂y) and temporal (∂p/∂t) derivatives of p.
• flow_type: Label indicating laminar or turbulent flow.

Simulation Details

• Laminar Flow: Generated using the analytical Poiseuille flow solution with added noise to ensure non-zero transverse velocities (v ≠ 0), mimicking realistic detector-like data.
• Turbulent Flow: Created by perturbing Poiseuille flow and evolving it with a basic Navier-Stokes solver, incorporating random noise to simulate turbulent behavior.
• Purpose: Designed to provide a balanced, compact dataset for PINN training, with derivatives included to enforce physics constraints in the loss function.

Format

• File: Stored as a CSV file (e.g., navier_stokes_flow.csv) in the data/ directory.
• Size: 10,000 rows, with columns for coordinates, velocities, pressure, derivatives, and flow type.

Source

The dataset is synthetically generated to emulate flow data for PINN training, inspired by methodologies in PINN research for solving the Navier-Stokes equations. It is curated for public use, enabling researchers to explore fluid dynamics modeling without access to expensive CFD simulations.

Use Cases

This dataset is a versatile resource for a range of applications:

• PINN Training: Train Physics-Informed Neural Networks to solve the Navier-Stokes equations for laminar and turbulent flows.
• Machine Learning: Develop models to predict velocity or pressure fields from spatial-temporal coordinates.
• Data Visualization: Create plots of flow fields (e.g., velocity streamlines, pressure contours) to study fluid behavior.
• Research: Investigate the differences between laminar and turbulent flows using ML or analytical methods.
• Education: Use in CFD or machine learning courses to teach PINN concepts and fluid dynamics.

Similar Datasets

Explore these related datasets for additional inspiration:

• CERN Proton Collision Dataset: Particle collision data for high-energy physics research. Link
• Airfoil Self-Noise Dataset: Acoustic data for aerodynamic studies. Link
• CERN Electron Collision Data: Electron collision events from CERN experiments. Link
• Wind Speed Prediction Dataset: Meteorological data for wind forecasting. Link
• Spanish Wine Quality Dataset: Chemical properties for wine quality classification. Link

Note: Links are placeholders as specific URLs were not provided. Replace with actual links if available.

Acknowledgements

We thank the computational fluid dynamics and machine learning communities for advancing PINN research, particularly the authors of the Physics-Informed Neural Networks for Solving the Navier-Stokes Equation paper for inspiring this dataset. The synthetic data was generated to support open science and education, drawing on simplified Navier-Stokes simulations.

For more information about PINNs, explore resources like: https://maziarraissi.github.io/PINNs/

License

MIT License (see LICENSE file for details).

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Have questions or ideas? Open a GitHub issue or join the discussion on Hugging Face. Happy exploring the flow of fluids!