Update README with simplified dataset card (removed tested models, acknowledgments, and extra usage examples)

README.md

@@ -24,11 +24,10 @@ tags:
 
 This dataset accompanies the research paper **"Pre-Generating Multi-Difficulty PDE Data For Few-Shot Neural PDE Solvers"** (under review at ICLR 2026). It contains systematically generated 2D incompressible Navier-Stokes fluid flow simulations designed to study **difficulty transfer** in neural PDE solvers.
 
-The key insight: by pre-generating many low and medium difficulty examples and including them with a small number of hard examples, neural PDE solvers can learn high-difficulty physics from far fewer samples. This dataset enables **8.9× reduction in compute time** while achieving comparable performance.
+The key insight: by pre-generating many low and medium difficulty examples and including them with a small number of hard examples, neural PDE solvers can learn high-difficulty physics from far fewer samples.
 
 ### Dataset Summary
 
-- **Total Size:** ~421 GB
 - **Format:** NumPy arrays (.npy files)
 - **Number of Files:** 9
 - **Simulations per file:** 6,400 trajectories
@@ -37,21 +36,6 @@ The key insight: by pre-generating many low and medium difficulty examples and i
 - **Solver:** OpenFOAM (icoFoam)
 - **Domain:** 2D Incompressible Navier-Stokes equations
 
-### Problem Setting
-
-The dataset solves the 2D incompressible Navier-Stokes equations:
-
-```
-∂u/∂t + (u · ∇)u + ∇p = ν∆u
-∇ · u = 0
-```
-
-where:
-- `u(x,t)` is the velocity field
-- `p(x,t)` is the kinematic pressure
-- `ν` is the kinematic viscosity (1.5 × 10⁻⁵ m²/s)
-- Domain: Ω ⊂ [0,1]²
-
 ## Difficulty Axes
 
 The dataset systematically varies complexity along three axes:
@@ -115,68 +99,8 @@ Each `.npy` file contains a NumPy array with shape: `(6400, 20, 128, 128, 6)`
 5. **Binary mask** - Geometry encoding (1 = obstacle, 0 = fluid)
 6. **SDF** - Signed distance field to nearest obstacle boundary
 
-## Simulation Details
-
-### Boundary Conditions
-
-**Flow Past Object (FPO):**
-- **Left (inlet):** Parabolic velocity profile with peak velocity Umax
-- **Right (outlet):** Zero-gradient pressure outlet
-- **Top/Bottom:** No-slip walls (u = 0)
-- **Obstacles:** No-slip walls (u = 0)
-
-### Reynolds Number Sampling
-Re is sampled from a truncated Gaussian distribution N(5000, 2000²) with support [100, 10000]. The inlet velocity is scaled to achieve the target Re:
-
-```
-Re = (U_avg × L) / ν
-U_avg = (2/3) × U_max
-```
-
-### Time Integration
-- **Scheme:** Backward Euler (1st order implicit)
-- **Spatial discretization:** Finite volume method
-- **Gradient terms:** Gauss linear (central differencing)
-- **Convection:** Gauss linearUpwind with gradient reconstruction
-- **Diffusion:** Gauss linear orthogonal
-
-### Simulation Duration
-Adaptive time scheduling based on Reynolds number to ensure flow development:
-- **Low Re (10-100):** Fixed 2700s
-- **Medium Re (100-1000):** 1-10× characteristic diffusion time
-- **High Re (1000-10000):** 10-40× characteristic diffusion time
-
-### Computational Cost
-The harder the simulation, the more expensive to generate:
-
-| Configuration | Average Time (seconds) |
-|--------------|----------------------|
-| No obstacle, Low Re | 176.7 |
-| No obstacle, Medium Re | 261.1 |
-| No obstacle, High Re | 350.4 |
-| One obstacle, Low Re | 609.5 |
-| One obstacle, Medium Re | 731.1 |
-| One obstacle, High Re | 942.8 |
-| Multiple obstacles, Low Re | 1550.9 |
-| Multiple obstacles, Medium Re | 1599.2 |
-| Multiple obstacles, High Re | 1653.3 |
-
-## Key Research Findings
-
-This dataset was specifically designed to study **difficulty transfer** in neural PDE solvers:
-
-1. **Sample Efficiency**: Training on 10% hard data + 90% easy/medium data recovers ~96-98% of the performance of training on 100% hard data
-
-2. **Compute Efficiency**: By mixing difficulties optimally, you can achieve the same error with **8.9× less compute** spent on data generation
-
-3. **Medium > Easy**: For most budgets, generating fewer medium-difficulty examples outperforms generating more easy examples
-
-4. **Foundation Dataset Potential**: Medium-difficulty data (single obstacle) improves few-shot performance on complex geometries (NURBS shapes from FlowBench)
-
 ## Usage
 
-### Basic Loading
-
 ```python
 import numpy as np
 from huggingface_hub import hf_hub_download
@@ -203,79 +127,6 @@ mask = trajectory_0[:, :, :, 4]  # Binary geometry mask
 sdf = trajectory_0[:, :, :, 5]  # Signed distance field
 ```
 
-### Difficulty Mixing for Training
-
-```python
-import numpy as np
-from huggingface_hub import hf_hub_download
-
-# Load different difficulty levels
-easy_data = np.load(hf_hub_download(
-    repo_id="sage-lab/PreGen-NavierStokes-2D",
-    filename="Geometry_Axis/FPO_Geometry_Easy_NoObstacle.npy",
-    repo_type="dataset"
-))
-
-medium_data = np.load(hf_hub_download(
-    repo_id="sage-lab/PreGen-NavierStokes-2D",
-    filename="Geometry_Axis/FPO_Geometry_Medium_SingleObstacle.npy",
-    repo_type="dataset"
-))
-
-hard_data = np.load(hf_hub_download(
-    repo_id="sage-lab/PreGen-NavierStokes-2D",
-    filename="Geometry_Axis/FPO_Geometry_Hard_MultiObstacle.npy",
-    repo_type="dataset"
-))
-
-# Recommended: Use 10% hard + 90% medium for cost-effective training
-n_hard = 80
-n_medium = 720
-
-train_data = np.concatenate([
-    hard_data[:n_hard],
-    medium_data[:n_medium]
-], axis=0)
-
-# Hold out 100 hard examples for testing
-test_data = hard_data[-100:]
-```
-
-### Computing Metrics
-
-```python
-def compute_nmae(y_true, y_pred):
-    """
-    Compute normalized Mean Absolute Error (nMAE)
-    as used in the paper.
-
-    Args:
-        y_true: Ground truth, shape (N, T, H, W, C)
-        y_pred: Predictions, shape (N, T, H, W, C)
-
-    Returns:
-        nMAE: Normalized mean absolute error
-    """
-    numerator = np.abs(y_true - y_pred).sum()
-    denominator = np.abs(y_true).sum()
-    return numerator / (denominator + 1e-10)
-```
-
-## Tested Models
-
-The paper evaluates this dataset on:
-
-### Supervised Neural Operators (trained from scratch)
-- **CNO** (Convolutional Neural Operator) - 18M parameters
-- **F-FNO** (Factorized Fourier Neural Operator) - 5-layer
-
-### Foundation Models (fine-tuned)
-- **Poseidon-T** (Tiny) - 21M parameters
-- **Poseidon-B** (Base) - 158M parameters
-- **Poseidon-L** (Large) - 629M parameters
-
-All models are trained autoregressively with one-step-ahead prediction (t → t+1) using relative L1 loss.
-
 ## Citation
 
 If you use this dataset, please cite:
@@ -292,34 +143,10 @@ If you use this dataset, please cite:
 
 **Note:** Citation will be updated once the paper is published.
 
-## Related Datasets
-
-- **The Well** - Large-scale multi-physics PDE dataset
-- **PDEBench** - Benchmark for scientific machine learning
-- **FlowBench** - Flow simulation over complex geometries (NURBS shapes)
-
 ## License
 
 MIT License
 
-## Acknowledgments
-
-This dataset was generated using:
-- **OpenFOAM** (v2406) for CFD simulations
-- Simulations performed on computational clusters
-- Total compute time: Several thousand GPU/CPU hours
-
-## Contact
-
-For questions or issues:
-- Open an issue in the dataset repository
-- Contact the sage-lab organization on Hugging Face
-- See the paper for additional contact information (once published)
-
-## Dataset Maintainers
-
-sage-lab organization
-
 ---
 
 **Dataset Version:** 1.0