Notebooks have hard-coded paths and some code does not work

[skalarproduktraum]

Big thanks for sharing the code! I have however encountered some issues:

• some files contain hardcoded paths:
  • NavierStokesEquation_Inverse_Problem.ipynb
  • QHOEquation_Forward_Problem_m=21.ipynb

I would have fixed that, but it's unclear to me whether PSM_V1 or PSM_V2 is needed in those cases.

In QHOEquation_Forward_Problem_m=21.ipynb, I have tried to replace the hardcoded path with both PSM versions, however V2 does not work already at the import level, and with V1, the cell

# Sobolev Cubature
diffeo_2d = hyper_rect(*rect)
diffeo_1d_0 = hyper_rect(rect[0])
diffeo_1d_1 = hyper_rect(rect[1])

sob_2d = Sobolev(deg=50, dim=2, diffeo=diffeo_2d)
sob_1d_0 = Sobolev(deg=200, diffeo=diffeo_1d_0)
sob_1d_1 = Sobolev(deg=200, diffeo=diffeo_1d_1)

dx2, dy2 = torch.tensor(sob_2d.diff.diffs(np.array([[2,0],[0,2]])))

leads to the error

---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
Cell In[12], line 6
      3 diffeo_1d_0 = hyper_rect(rect[0])
      4 diffeo_1d_1 = hyper_rect(rect[1])
----> 6 sob_2d = Sobolev(deg=50, dim=2, diffeo=diffeo_2d)
      7 sob_1d_0 = Sobolev(deg=200, diffeo=diffeo_1d_0)
      8 sob_1d_1 = Sobolev(deg=200, diffeo=diffeo_1d_1)

TypeError: __init__() got an unexpected keyword argument 'dim'