Upload README.md with huggingface_hub

README.md

@@ -0,0 +1,157 @@
+---
+license: apache-2.0
+task_categories:
+  - time-series-forecasting
+  - tabular-regression
+tags:
+  - physics
+  - pde
+  - fluid-dynamics
+  - simulation
+  - numerical-methods
+size_categories:
+  - 10K<n<100K
+---
+
+# INC Dataset: Implicit Neural Correction for PDE Solvers
+
+## Dataset Description
+
+This dataset contains simulation data for training and evaluating implicit neural correction methods for partial differential equation (PDE) solvers. The dataset includes two challenging dynamical systems demonstrating complex spatiotemporal behaviors:
+
+1. **Kuramoto-Sivashinsky (KS) Equation** - 1D chaotic dynamics
+2. **Backward-Facing Step (BFS) Flow** - 2D incompressible Navier-Stokes with complex geometry
+
+### Dataset Summary
+
+- **Repository**: [INC: Implicit Neural Correction for PDE Solvers](https://github.com/tum-pbs/INC)
+- **Paper**: [INC: An Indirect Neural Corrector for Auto-Regressive Hybrid PDE Solvers](https://openreview.net/forum?id=s3Uk3lrfjy) (NeurIPS 2025)
+
+## Dataset Structure
+
+```
+INC_Data/
+├── KS/
+│   └── Dataset/
+│       ├── train/
+│       ├── valid/
+│       └── test/
+└── BFS/
+    └── Dataset/
+    │   ├── train/
+    │   ├── valid/
+    │   └── test/
+    └── Results/
+        └── NoModel/        # Baseline without correction
+        └── INC_SmallCNN/
+            └── {timestamp}_mstep8_.../ # an example model
+```
+There are two main subdirectories corresponding to the two PDE systems, each containing training, validation, and test datasets. For BFS, there is also a `Results` directory showcasing baseline and corrected model results.
+
+### Data Fields
+
+Each dataset contains time-series simulation data with the following characteristics:
+
+
+#### Kuramoto-Sivashinsky Equation
+- **Spatial Resolution**: 64 grid points
+- **Temporal Resolution**: dt = 0.01
+- **Physical Domain**: [0, 22]
+- **Parameters**: Periodic boundary conditions
+- **File Format**: `.pth` (PyTorch dictionary with trajectories and metadata)
+- **Data Structure**: 
+  - `trajectories`: shape `(num_trajectories, time_steps, spatial_points)` = `(27, 10001, 64)` for train
+  - `domain_size`: shape `(num_trajectories,)` = `(27,)` 
+  - `metadata`: dict with generation parameters (gen_dt, resolution, time_scheme, etc.)
+- **Dataset Sizes**:
+  - Train: 27 trajectories × 10,001 timesteps
+  - Valid: 3 trajectories × 10,001 timesteps
+  - Test: 6 trajectories × 10,001 timesteps
+
+#### Backward-Facing Step (BFS)
+- **Spatial Resolution**: Multi-block grid with refinement, downsampled to approximately $128 \times 32$
+- **Temporal Resolution**: Saved with fixed intervals (dt = 0.1)
+- **Physical Domain**: 2D channel with backward-facing step geometry (5 blocks)
+- **Parameters**: Reynolds numbers {1300, 1350, 1400}, Step height {0.85, 0.875, 1.0}
+- **File Format**: Combined `.json` (metadata) + `.npz` (tensor data) per timestep
+- **Data Structure**:
+  - Each configuration has 5 blocks with varying resolutions
+  - Block shapes vary by position: e.g., `(1, 2, 16, 16)` for velocity, `(1, 1, 16, 16)` for pressure
+  - Metadata includes: domain name, spatial dimensions, viscosity, block info, boundaries
+  - Data arrays: velocity (2 channels), pressure (1 channel), vertex coordinates, boundary conditions
+- **Dataset Sizes**:
+  - Train: 3 configurations × ~801 timesteps each
+  - Valid: 1 configuration × 301 timesteps
+  - Test: 1 configuration × 3,001 timesteps
+
+
+## Dataset Generation
+
+The data was generated using classical numerical PDE solvers:
+
+- **Burgers**: 5th-order WENO scheme with RK4 time integration
+- **Kuramoto-Sivashinsky**: Pseudo-spectral method with exponential time differencing
+- **BFS**: PISO algorithm with custom CUDA implementation for multi-block domains
+
+### Generation Scripts
+
+The original data generation code is available in the [INC repository](https://github.com/tum-pbs/INC):
+- `scripts/Sim_BFS.py` - Generate BFS flow data
+- `solvers/solver_1d.py` - Contains Burgers and KS solvers
+
+## Use Cases
+
+This dataset is designed for:
+
+1. **Hybrid Physics-ML Models**: Training neural networks to correct numerical solver errors
+2. **Operator Learning**: Learning mappings between PDE solution spaces
+3. **Time-Series Forecasting**: Predicting long-term evolution of chaotic dynamical systems
+4. **Benchmarking**: Evaluating neural PDE solver architectures (FNO, U-Net, DeepONet)
+5. **Physics-Informed Learning**: Combining data-driven and physics-based approaches
+
+
+See the [paper](https://openreview.net/forum?id=s3Uk3lrfjy) for detailed results and methodology.
+
+## Citation
+
+If you use this dataset in your research, please cite:
+
+```bibtex
+@article{INC2025,
+  title={{INC}: An Indirect Neural Corrector for Auto-Regressive Hybrid {PDE} Solvers},
+  author={Hao Wei, Aleksandra Franz, Björn Malte List, Nils Thuerey},
+  booktitle={The Thirty-ninth Annual Conference on Neural Information Processing Systems},
+  year={2025},
+  url={https://openreview.net/forum?id=s3Uk3lrfjy}
+}
+```
+
+## Limitations and Biases
+
+- **Domain Specificity**: Dataset is limited to three specific PDEs; generalization to other equations may require additional data
+- **Resolution Trade-off**: Coarser resolutions improve computational efficiency but may miss fine-scale features
+- **Boundary Conditions**: Limited to periodic (KS) and no-slip wall (BFS) boundaries
+- **Parameter Range**: Limited range of physical parameters (viscosity, Reynolds number, domain geometry)
+
+## Additional Information
+
+### Licensing
+
+This dataset is released under the Apache 2.0 License. You are free to use, modify, and distribute the data with proper attribution.
+
+### Contact
+
+For questions or issues with the dataset:
+- **GitHub Issues**: [INC Repository](https://github.com/tum-pbs/INC/issues)
+
+### Acknowledgments
+
+This work builds upon numerical methods and deep learning architectures from:
+- PICT solver (Franz et al., 2025)
+- Fourier Neural Operator (Li et al., 2020)
+- DeepONet (Lu et al., 2021)
+
+
+---
+
+**For detailed usage instructions and training examples, see the [main repository](https://github.com/tum-pbs/INC).**