One-dimensional Kuramoto Sivashinsky equation.

One-dimensional Kuramoto Sivashinsky equation; generated using the method of lines, with the spatial derivatives computed using the pseudo-spectral method.
We set T = 100 for the training (and T = 200 for validation and testing) data, with ∆t = 0.2. Further, we set X = [0, 64], with ∆x = 0.25. Initial conditions were sampled from a distribution over the truncated Fourier series with random coefficients. Finally, we set periodic boundary conditions.

The dataset contains 2048 trajectories for the training dataset, and 128 trajectories for each of the validation and testing datasets. For each trajectory, the first 360 steps were considered to be part of the warmup phase and subsequently discarded. The data was generated using double-precision floating point format (float64). It is recommended to convert the data into single-precision floating-point format (float32).

KS_test_02.h5

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KS_train_2048_02.h5

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KS_valid_02.h5

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