| --- |
| 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. |
|
|
