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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.
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