Range of the x-coordinate for 1D Burgers data

[functoreality]

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).

However, in Fig.7, the range is (-1, 1) according to the curves, and (0, 1) according to the two-dimensional plot.

In the configuration files for data generation, the range appears to be (-1, 1) as well:

PDEBench/pdebench/data_gen/data_gen_NLE/BurgersEq/config/multi/1e-2.yaml

Lines 6 to 7 in 4361430

	xL: -1.
	xR: 1.

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:

PDEBench/pdebench/data_gen/data_gen_NLE/BurgersEq/burgers_multi_solution_Hydra.py

Lines 265 to 266 in 4361430

	f_upwd = (fR[1:cfg.multi.nx+2] + fL[2:cfg.multi.nx+3]
	- 0.5*jnp.abs(uL[2:cfg.multi.nx+3] + uR[1:cfg.multi.nx+2])*(uL[2:cfg.multi.nx+3] - uR[1:cfg.multi.nx+2]))

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.

[kmario23]

Thank you for bringing this up! We have implemented the fix in the latest commit 5f19987

The new dataset and results will be updated in the next upload of the paper.