Centrum-IntelliPhysics/PDEControl_DPC

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
• 💻 Code: 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:

$$f(x,t)=\sum _{i=1}^{n_c}{c}_i(t)\exp \text{\hspace{0.17em}⁣}(-\frac{(x-x_i{)}^2}{2{\sigma }^2})f(x,t)\; =\; \backslash sum\_\{i=1\}^\{n\_c\}\; c\_i(t)\backslash ,\backslash exp\backslash !\backslash left(-\backslash frac\{(x\; -\; x\_i)^2\}\{2\backslash sigma^2\}\backslash right)$$

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

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:

cd HE_TT && python train_ti_don.py --epochs 120000

To load one directly:

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

@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.