Dataset Card for base-mixedp-ic16

This one of several datasets we used for training our scaled-up Panda-72M model (https://huggingface.co/GilpinLab/panda-72M) of Panda: Patched Attention for Nonlinear Dynamics.

Details: Each subdirectory is the named as {Base System}-pp{param_idx} where the param_idx is the index of the specific parameter perturbation. The files in each subdirectory correspond to different initial conditions, all with different number of "periods" on Fourier timescale. Specifically, we provide 16 initial conditions (each with different number of periods) for each parameter perturbation.

NOTE (on historical changelog): The dataset in train.parquet is a result of us combining two data directories, “train” and “train_more” which used to exist separately on our servers. We combined these two splits to provide the community with a more complete dataset for future works. We clarify that “train_more” is generated exactly the same way as “train”; however, “train_more” contains 9 initial conditions (ic8-ic16) per perturbed system whereas “train” contains 7 initial conditions (ic1-ic7) per perturbed system. This discrepancy was due to an indexing error. Moreover, there are actually only 109 “ic1” trajectories in the entire “train” dataset; these are all for “pp0” i.e. the unperturbed original base systems.

We emphasize that we trained Panda-72M on only this original “train” split, not on “train_more”. For more details, wandb run log, and book-keeping, see GilpinLab/dataset-panda72M-repro (https://huggingface.co/datasets/GilpinLab/dataset-panda72M-repro) which contains the parquet files of the exact splits we used in our training.

Below, we provide a breakdown of the original composition of these two splits, which we subsequently combined into train.parquet (simply by taking the union of all files):

	files	base systems	(system, pp) pairs i.e. number of perturbed systems
train/	32,996	112	5,781
train_more/	49,227	111	5,805

The tables below give the number of trajectories for each initial condition (ic{1-16}) in the original two dataset splits that we combined into "train.parquet". Each ic{1-16} has fewer than the number of perturbed systems because some trajectories may not have passed our fixed integration time-limit, or our filters.

train

ic1	ic2	ic3	ic4	ic5	ic6	ic7
109	5461	5467	5487	5477	5512	5483

train_more

ic8	ic9	ic10	ic11	ic12	ic13	ic14	ic15	ic16
5492	5437	5412	5470	5480	5476	5465	5493	5502

Paper abstract:

Chaotic systems are intrinsically sensitive to small errors, challenging efforts to construct predictive data-driven models of real-world dynamical systems such as fluid flows or neuronal activity. Prior efforts comprise either specialized models trained separately on individual time series, or foundation models trained on vast time series databases with little underlying dynamical structure. Motivated by dynamical systems theory, we present Panda, Patched Attention for Nonlinear DynAmics. We train Panda on a novel synthetic, extensible dataset of 2 \times 10^4 chaotic dynamical systems that we discover using an evolutionary algorithm. Trained purely on simulated data, Panda exhibits emergent properties: zero-shot forecasting of unseen real world chaotic systems, and nonlinear resonance patterns in cross-channel attention heads. Despite having been trained only on low-dimensional ordinary differential equations, Panda spontaneously develops the ability to predict partial differential equations without retraining. We demonstrate a neural scaling law for differential equations, underscoring the potential of pretrained models for probing abstract mathematical domains like nonlinear dynamics.

• Preprint: arXiv:2505.13755
• Repository: https://github.com/abao1999/panda

Citation

BibTeX:

If you find our work valuable for your research, please cite us:

@misc{lai2025panda,
      title={Panda: A pretrained forecast model for universal representation of chaotic dynamics}, 
      author={Jeffrey Lai and Anthony Bao and William Gilpin},
      year={2025},
      eprint={2505.13755},
      archivePrefix={arXiv},
      primaryClass={cs.LG},
      url={https://arxiv.org/abs/2505.13755}, 
}