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README.md

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 ---
 license: mit
+task_categories:
+  - other
+tags:
+  - pde
+  - optimal-control
+  - operator-learning
+  - deeponet
+  - differentiable-predictive-control
+  - scientific-machine-learning
+pretty_name: PDE Control with DPC and Time-Integrated Neural Operators
+size_categories:
+  - 1K<n<10K
 ---
+
+# PDE Control — TI-DeepONet Training Datasets
+
+Simulation datasets for **"Learning to Control PDEs with Differentiable Predictive Control
+and Time-Integrated Neural Operators"**.
+
+- 📄 Paper: [arXiv:2511.08992](https://arxiv.org/abs/2511.08992)
+- 💻 Code: [github.com/Centrum-IntelliPhysics/PDEControl_DPC](https://github.com/Centrum-IntelliPhysics/PDEControl_DPC)
+
+These are the trajectory datasets used to train the **TI-DeepONet surrogates**. Each file
+holds 3000 controlled trajectories generated by a classical numerical solver under randomly
+sampled control sequences.
+
+> **You may not need these.** The pretrained checkpoints are committed in the code
+> repository, and both notebooks in each experiment directory run without any download.
+> You need these files only to retrain a surrogate from scratch.
+
+## Files
+
+| File | System | Size | Trajectories | Timesteps | Controls |
+|---|---|---|---|---|---|
+| `heat_dataset_dpc.npz` | 1D heat equation | 895 MB | 3000 | 401 | 4 |
+| `burgers_smooth_f_dataset.npz` | 1D Burgers' equation | 670 MB | 3000 | 301 | 2 |
+| `reaction_diffusion_dataset200.npz` | 1D reaction–diffusion | 893 MB | 3000 | 401 | 4 |
+
+All arrays are `float64`. Spatial resolution is $N = 100$ on $x \in [0,1]$ with
+$\Delta t = 10^{-3}$ throughout.
+
+## Contents
+
+Each `.npz` contains:
+
+| Key | Shape | Meaning |
+|---|---|---|
+| `solutions` | `(3000, T+1, 100)` | state trajectories $u(x,t)$ |
+| `controls` | `(3000, T, n_c)` | control amplitudes $c_i(t)$ |
+| `x` | `(100,)` | spatial grid, `linspace(0, 1, 100)` |
+| `dt` | scalar | time step, `1e-3` |
+
+Plus per-system physical parameters:
+
+- **heat** — `nu` (diffusivity, 0.1), `centers` (4 actuator positions), `sigma` (actuator width)
+- **burgers** — no extra keys; actuator geometry lives in the code's `config.py`
+- **reaction–diffusion** — `D` (diffusivity, 0.01), `r` (reaction rate, 1.0), `centers`, `sigma`
+
+Control enters every system as a sum of Gaussian sources:
+
+$$f(x,t) = \sum_{i=1}^{n_c} c_i(t)\,\exp\!\left(-\frac{(x - x_i)^2}{2\sigma^2}\right)$$
+
+## Generation
+
+| System | Solver |
+|---|---|
+| Heat | Crank–Nicolson |
+| Burgers' | Upwind advection + forward Euler |
+| Reaction–diffusion | Backward Euler + Newton iteration, Neumann BCs |
+
+The generating scripts are in the code repository (`heat_1D_gen.py`,
+`Burgers_1D_smooth_f_gen.py`, `RD_1D_gen2.py`), so every file here is reproducible from
+source.
+
+## Usage
+
+```bash
+git clone https://github.com/Centrum-IntelliPhysics/PDEControl_DPC.git
+cd PDEControl_DPC
+pip install -r requirements.txt
+
+python download_data.py            # all three
+python download_data.py heat       # or just one
+```
+
+Files land where each `config.py` expects them. Then:
+
+```bash
+cd HE_TT && python train_ti_don.py --epochs 120000
+```
+
+To load one directly:
+
+```python
+import numpy as np
+d = np.load("heat_dataset_dpc.npz")
+print(d["solutions"].shape)   # (3000, 401, 100)
+print(d["controls"].shape)    # (3000, 400, 4)
+```
+
+## Citation
+
+```bibtex
+@misc{sarkar2025learningcontrolpdesdifferentiable,
+      title={Learning to Control PDEs with Differentiable Predictive Control and Time-Integrated Neural Operators},
+      author={Dibakar Roy Sarkar and Ján Drgoňa and Somdatta Goswami},
+      year={2025},
+      eprint={2511.08992},
+      archivePrefix={arXiv},
+      primaryClass={cs.CE},
+      url={https://arxiv.org/abs/2511.08992},
+}
+```
+
+## License
+
+MIT, matching the code repository.