Update README.md

README.md

@@ -1,3 +1,89 @@
----
-license: apache-2.0
----
+---
+title: Navier-Stokes Simulated Flow Dataset for PINNs
+emoji: 🌊
+license: mit
+tags:
+  - computational-fluid-dynamics
+  - physics-informed-neural-networks
+  - navier-stokes
+  - machine-learning
+  - fluid-dynamics
+---
+
+# 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).
+
+---
+
+Have questions or ideas? Open a GitHub issue or join the discussion on Hugging Face. Happy exploring the flow of fluids!
+
+