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README.md

@@ -1,4 +1,26 @@
 ---
+language:
+- en
+license: cc-by-4.0
+pretty_name: Navier-Stokes Analytical Benchmark
+tags:
+- physics
+- fluid-dynamics
+- navier-stokes
+- computational-fluid-dynamics
+- scientific-computing
+- benchmark
+task_categories:
+- other
+size_categories:
+- n<1K
+annotations_creators:
+- expert-generated
+configs:
+- config_name: default
+  data_files:
+  - split: train
+    path: data/train-*
 dataset_info:
   features:
   - name: name
@@ -10,26 +32,184 @@ dataset_info:
   - name: rayleigh_number
     dtype: float64
   - name: grid_shape
-    sequence: int32
+    sequence:
+      dtype: int32
   - name: u_field
-    sequence: float32
+    sequence:
+      dtype: float32
   - name: v_field
-    sequence: float32
+    sequence:
+      dtype: float32
   - name: t_field
-    sequence: float32
+    sequence:
+      dtype: float32
   - name: p_field
-    sequence: float32
+    sequence:
+      dtype: float32
   - name: latex_equation
     dtype: string
-  splits:
-  - name: train
-    num_bytes: 5085305
-    num_examples: 77
-  download_size: 970522
-  dataset_size: 5085305
-configs:
-- config_name: default
-  data_files:
-  - split: train
-    path: data/train-*
 ---
+
+# Navier-Stokes Analytical Benchmark
+
+A dataset of 2D incompressible fluid dynamics problems with **closed-form analytical solutions** on a 64x64 grid. Intended as ground-truth supervision for physics-informed neural networks (PINNs), neural operators (FNO, DeepONet), and other scientific ML models.
+
+Every sample provides velocity (u, v), pressure (p), and temperature (T) fields computed directly from exact or series-expansion solutions to the Navier-Stokes and energy equations -- no numerical solver is involved.
+
+## Dataset Description
+
+- **Repository:** [C3S2-Lab/navier-stokes-benchmark](https://huggingface.co/datasets/C3S2-Lab/navier-stokes-benchmark)
+- **Size:** 77 samples
+- **Grid:** 64 x 64, uniform spacing on [0, 1]^2
+- **Fields per sample:** u (horizontal velocity), v (vertical velocity), T (temperature), p (pressure)
+- **Format:** Apache Arrow / Parquet
+
+## Flow Types
+
+### 1. Poiseuille (Channel) Flow -- 24 samples
+
+Fully-developed pressure-driven flow between parallel plates. Exact parabolic velocity profile.
+
+$$u(y) = \frac{Re}{2}\left(-\frac{dP}{dx}\right) y(1-y), \quad v = 0, \quad p(x) = \frac{dP}{dx}\, x$$
+
+| Parameter | Values |
+|---|---|
+| Re | 1, 10, 50, 100, 200, 500, 1000, 2000 |
+| dP/dx | -0.5, -1.0, -2.0 |
+
+### 2. Lid-Driven Cavity -- 6 samples
+
+Square cavity with a moving top wall in the Stokes (creeping-flow) limit. Stream function expressed as a truncated Fourier-sinh series (8 terms).
+
+$$\nabla^4 \psi = 0, \quad \psi = \sum_{n=1}^{N} c_n \frac{\sinh(n\pi y)}{\sinh(n\pi)} \sin(n\pi x)$$
+
+| Parameter | Values |
+|---|---|
+| Re | 0.01, 0.1, 1.0, 10.0, 50.0, 100.0 |
+| U_lid | 1.0 |
+
+### 3. Rayleigh-Benard Convection -- 32 samples
+
+Linear onset eigenmodes of buoyancy-driven convection between heated plates. Critical Rayleigh number Ra_c ~ 1708 for rigid-rigid boundaries.
+
+$$\frac{\partial \mathbf{u}}{\partial t} + (\mathbf{u}\cdot\nabla)\mathbf{u} = -\nabla p + Pr\,\nabla^2\mathbf{u} + Ra\,Pr\,T\,\hat{z}$$
+
+| Parameter | Values |
+|---|---|
+| Ra | 500, 1000, 1708, 2000, 5000, 10000, 50000, 100000 |
+| Pr | 0.1, 0.71, 1.0, 7.0 |
+
+### 4. Buoyancy Plume -- 15 samples
+
+Self-similar Gaussian profile for a laminar free-convection plume above a line heat source.
+
+$$w(\eta) \sim \frac{\sqrt{Ra\,Q}}{x^{1/2}} e^{-\eta^2}, \quad T(\eta) \sim \frac{Q}{x^{3/4}} e^{-Pr\,\eta^2}, \quad \eta = \frac{y}{x^{3/4}}$$
+
+| Parameter | Values |
+|---|---|
+| Ra | 1000, 5000, 10000, 50000, 100000 |
+| Pr | 0.71, 1.0, 7.0 |
+
+## Dataset Schema
+
+| Field | Type | Description |
+|---|---|---|
+| `name` | `string` | Unique identifier (e.g. `poiseuille_Re100`) |
+| `description` | `string` | Human-readable description of the flow configuration |
+| `parameters` | `string` (JSON) | Physical parameters (`Re`, `Ra`, `Pr`, `dpdx`, etc.) |
+| `rayleigh_number` | `float64` | Rayleigh number (`null` for isothermal flows) |
+| `grid_shape` | `Sequence[int32]` | `[64, 64]` spatial resolution |
+| `u_field` | `Sequence[float32]` | Horizontal velocity, flattened (4096 values) |
+| `v_field` | `Sequence[float32]` | Vertical velocity, flattened |
+| `t_field` | `Sequence[float32]` | Temperature field, flattened (zeros if isothermal) |
+| `p_field` | `Sequence[float32]` | Pressure field, flattened |
+| `latex_equation` | `string` | LaTeX governing equations / analytical solution |
+
+All field arrays are stored flat and should be reshaped to `grid_shape` (64 x 64) for use.
+
+## Usage
+
+### Load from the Hub
+
+```python
+from datasets import load_dataset
+
+ds = load_dataset("C3S2-Lab/navier-stokes-benchmark")
+```
+
+### Convert to PyTorch tensors
+
+```python
+ds.set_format("torch", columns=["u_field", "v_field", "t_field", "p_field"])
+
+sample = ds["train"][0]
+u = sample["u_field"].reshape(64, 64)
+```
+
+### Filter by flow regime
+
+```python
+# Supercritical Rayleigh-Benard cases only
+rb = ds["train"].filter(
+    lambda x: x["rayleigh_number"] is not None and x["rayleigh_number"] > 1708
+)
+```
+
+### Generate locally
+
+```bash
+pip install numpy datasets
+python generate_ns_dataset.py
+```
+
+This creates `ns_dataset/` (Arrow format) and `ns_dataset.parquet`.
+
+### Push to the Hub
+
+```bash
+python generate_ns_dataset.py --push --repo C3S2-Lab/navier-stokes-benchmark
+```
+
+| Flag | Default | Description |
+|---|---|---|
+| `--save` | `ns_dataset` | Local save directory |
+| `--push` | off | Push to HuggingFace Hub after generation |
+| `--repo` | `C3S2-Lab/navier-stokes-benchmark` | Target HuggingFace repository |
+
+## Dataset Creation
+
+All fields are computed from exact analytical solutions or truncated series expansions of the incompressible Navier-Stokes equations. No numerical PDE solver is used. The solutions cover:
+
+- **Poiseuille:** Exact closed-form solution to the steady momentum equation.
+- **Lid-driven cavity:** Biharmonic stream function series (Shankar & Deshpande, 2000), valid in the Stokes limit.
+- **Rayleigh-Benard:** Linear stability eigenmodes at/near the critical Rayleigh number (rigid-rigid boundaries).
+- **Buoyancy plume:** Gebhart similarity solution with Gaussian self-similar profiles.
+
+Grid: uniform 64x64 on the unit square [0, 1]^2 (plume domain shifted to x in [0.1, 1.0] to avoid the source singularity).
+
+## Intended Use
+
+- Supervised training and validation of physics-informed neural networks (PINNs)
+- Benchmarking neural operator architectures (FNO, DeepONet, etc.)
+- Evaluating equation-discovery and symbolic regression methods (via `latex_equation`)
+- Teaching and educational demonstrations of canonical fluid flows
+
+## Limitations
+
+- All solutions are 2D, steady-state, and incompressible.
+- Lid-driven cavity uses a Stokes-limit approximation; accuracy degrades for Re >> 1.
+- Rayleigh-Benard fields are linear-onset eigenmodes, not fully nonlinear convection rolls.
+- The 64x64 resolution is coarse for capturing sharp gradients at high Re or Ra.
+- Temperature fields are zero-filled for isothermal flows (Poiseuille, lid-driven cavity).
+
+## Citation
+
+```bibtex
+@dataset{c3s2lab_navier_stokes_benchmark,
+  title   = {Navier-Stokes Analytical Benchmark},
+  author  = {C3S2-Lab},
+  year    = {2026},
+  url     = {https://huggingface.co/datasets/C3S2-Lab/navier-stokes-benchmark},
+  note    = {Analytical solutions for 2D incompressible fluid dynamics}
+}
+```