Range of the x-coordinate for 1D Burgers data

Thank you a lot for this benchmark dataset. In Appendix D.3 of the paper, the range of the x-axis is (0, 1) according to equation (11,12). Screenshot_20231027_104930 However, in Fig.7, the range is (-1, 1) according to the curves, and (0, 1) according to the two-dimensional plot. Screenshot_20231027_103936 In the configuration files for data generation, the range appears to be (-1, 1) as well: https://github.com/pdebench/PDEBench/blob/4361430bd3704914ff6ed4fd737aaeb272354f19/pdebench/data_gen/data_gen_NLE/BurgersEq/config/multi/1e-2.yaml#L6-L7 For the dataset I downloaded:

with h5py.File('1D_Burgers_Sols_Nu0.01.hdf5', "r") as h5_file:
    print(h5_file['x-coordinate'][:])
# [-0.99902344 -0.9970703  -0.9951172  ...  0.9951172   0.9970703   0.99902344]

This seems a bit confusing to me.

Furthermore, if the range of the x-axis is (-1, 1), then I find a scaling issue similar to the Advection data mentioned here. If I have not misunderstood, for the Burgers equation, the shock propagates at a speed of (uL + uR) / 2. According to the first panel of Fig.7, the average of uL and uR is approximately -0.8, but the propagation speed seems to be doubled. I wonder whether this is related to the following lines in the data generation script: https://github.com/pdebench/PDEBench/blob/4361430bd3704914ff6ed4fd737aaeb272354f19/pdebench/data_gen/data_gen_NLE/BurgersEq/burgers_multi_solution_Hydra.py#L265-L266 In the updated script for the Advection equation, the value of the flux is multiplied by 0.5, but this operation is not applied here for the Burgers equation.

Thanks in advance for your response.

pdebench / PDEBench

Range of the x-coordinate for 1D Burgers data #51