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Zakharov–Kuznetsov Equation Dataset
Dataset Summary
This dataset contains numerical solutions to the Zakharov–Kuznetsov (ZK) equation, a multidimensional generalization of the Korteweg–de Vries (KdV) equation that models nonlinear wave propagation in magnetized plasma. The solutions were generated using a sixth-order Gauss–Legendre time integrator and sixth-order central finite differences for spatial derivatives.
The computational domain is discretized on a 128 × 128 grid in space and evolved until final time ( T = 2 ) using a time step ( \Delta t = 2/256 ). Each trajectory consists of 32 evenly spaced temporal snapshots.
The initial conditions consist of two interacting waves with randomized locations and amplitudes, allowing for diverse nonlinear dynamics and wave interactions suitable for operator learning and physics-informed machine learning research.
Dataset Structure
- Train/Validation/Test split: 700 / 150 / 150 trajectories
- Spatial resolution: 128 × 128
- Temporal snapshots: 32
- Integration scheme: 6th-order Gauss–Legendre (time), 6th-order central differences (space)
- Final time: T = 2
- Time step: Δt = 2/256
- Variables stored: Wave field ( u(x, y, t) )
Each dataset entry contains:
data: 2D array of shape(32, 128 * 128)representing the wave field over time. Has to be reshaped into(32, 128, 128)
Usage
from datasets import load_dataset
train_dataset = load_dataset("eirikfagerbakke/zk", split="train").with_format("numpy")
val_dataset = load_dataset("eirikfagerbakke/zk", split="validation").with_format("numpy")
test_dataset = load_dataset("eirikfagerbakke/zk", split="test").with_format("numpy")
Example access:
example = train_dataset[0]
u = example["data"].reshape(32, 128, 128)
u0 = u[0]
Applications
This dataset is designed for research in:
- Operator learning (e.g., DeepONet, FNO, Neural Operators)
Citation
If you use this dataset, please cite:
Eirik Fagerbakke, Zakharov–Kuznetsov Equation Dataset, 2025. Available on Hugging Face: eirikfagerbakke/zk
License
This dataset is released under the MIT License.
Acknowledgements
Generated as part of research on physics-informed deep learning and operator learning frameworks.
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