fix: remove uses of issymbollike, depend on SII

[AayushSabharwal]

Checklist

• Appropriate tests were added
• Any code changes were done in a way that does not break public API
• All documentation related to code changes were updated
• The new code follows the
  contributor guidelines, in particular the SciML Style Guide and
  COLPRAC.
• Any new documentation only uses public API

Additional context

Add any other context about the problem here.

[codecov]

Codecov Report

Attention: 3 lines in your changes are missing coverage. Please review.

Comparison is base (172cdc4) 84.99% compared to head (823a3b2) 82.69%.

Files	Patch %	Lines
src/interface/solution/common.jl	40.00%	3 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##           master     #346      +/-   ##
==========================================
- Coverage   84.99%   82.69%   -2.30%     
==========================================
  Files          41       41              
  Lines        1959     1959              
==========================================
- Hits         1665     1620      -45     
- Misses        294      339      +45     

☔ View full report in Codecov by Sentry.
📢 Have feedback on the report? Share it here.

[xtalax]

Solutions are coming out different, not sure why

[xtalax]

I will fix tomorrow

[cmhyett]

I've been digging into this, it seems like the PDESolution interface is fine, but the tests compare against a sol.original_sol and I believe the interpolation error actually exists here.

To show there isn't actually a difference in the interior solution, see the plots:

And the numerical difference:

julia> sol[u(t,x,y)][1,:,:] .- traditional_sol[1,:,:]
9×9 Matrix{Float64}:
 -0.0438214  -0.0438214  -0.0438214  -0.0438214  -0.0438214  -0.0438214  -0.0438214  -0.0438214  -0.0438214
 -0.0438214   0.0         0.0         0.0         0.0         0.0         0.0         0.0         0.0
 -0.0438214   0.0         0.0         0.0         0.0         0.0         0.0         0.0         0.0
 -0.0438214   0.0         0.0         0.0         0.0         0.0         0.0         0.0         0.0
 -0.0438214   0.0         0.0         0.0         0.0         0.0         0.0         0.0         0.0
 -0.0438214   0.0         0.0         0.0         0.0         0.0         0.0         0.0         0.0
 -0.0438214   0.0         0.0         0.0         0.0         0.0         0.0         0.0         0.0
 -0.0438214   0.0         0.0         0.0         0.0         0.0         0.0         0.0         0.0
 -0.0438214   0.0         0.0         0.0         0.0         0.0         0.0         0.0         0.0

julia> sol[u(t,x,y)][end,:,:] .- traditional_sol[end,:,:]
9×9 Matrix{Float64}:
  0.013751    -0.00170683  0.0141994  0.0140295  0.0135991  0.01192  0.0154102  0.0238034  -0.00906672
 -0.00039773   0.0         0.0        0.0        0.0        0.0      0.0        0.0         0.0
  0.0503736    0.0         0.0        0.0        0.0        0.0      0.0        0.0         0.0
  0.395711     0.0         0.0        0.0        0.0        0.0      0.0        0.0         0.0
  1.56715      0.0         0.0        0.0        0.0        0.0      0.0        0.0         0.0
 -0.312651     0.0         0.0        0.0        0.0        0.0      0.0        0.0         0.0
 -0.217997     0.0         0.0        0.0        0.0        0.0      0.0        0.0         0.0
 -0.0124258    0.0         0.0        0.0        0.0        0.0      0.0        0.0         0.0
 -0.00906672   0.0         0.0        0.0        0.0        0.0      0.0        0.0         0.0

If someone could point me to where this sol.original_sol is calculated, perhaps I could root-cause the issue.

[cmhyett]

Ah, so there are some dubious calls in the failing test MethodOfLines/test/components/solution_interface.jl:42

grid = get_discrete(pdesys, discretization) #(9,9)
traditional_sol = zeros(Float64, length(sol.t), 9, 9)
solu = sol.original_sol[grid[u(t, x, y)]]

but sol.original_sol is only (T, 8, 8), and we're indexing into it with a (9,9). It seems like it's just repeating the u(t,x,y)[2,2] value for the boundaries.

julia> traditional_sol[1,:,:]
9×9 Matrix{Float64}:
 0.0438214  0.0438214    0.0438214    0.0438214    …  0.0438214    0.0438214    0.0438214    0.0438214
 0.0438214  0.0438214    0.456629     0.99737         0.0438214    0.000881502  3.71685e-6   3.28505e-9
 0.0438214  0.456629     0.99737      0.456629        0.000881502  3.71685e-6   3.28505e-9   6.08589e-13
 0.0438214  0.99737      0.456629     0.0438214       3.71685e-6   3.28505e-9   6.08589e-13  2.36331e-17
 0.0438214  0.456629     0.0438214    0.000881502     3.28505e-9   6.08589e-13  2.36331e-17  1.92368e-22
 0.0438214  0.0438214    0.000881502  3.71685e-6   …  6.08589e-13  2.36331e-17  1.92368e-22  3.28215e-28
 0.0438214  0.000881502  3.71685e-6   3.28505e-9      2.36331e-17  1.92368e-22  3.28215e-28  1.17382e-34
 0.0438214  3.71685e-6   3.28505e-9   6.08589e-13     1.92368e-22  3.28215e-28  1.17382e-34  8.79946e-42
 0.0438214  3.28505e-9   6.08589e-13  2.36331e-17     3.28215e-28  1.17382e-34  8.79946e-42  1.3827e-49

julia> traditional_sol[10,:,:]
9×9 Matrix{Float64}:
 0.0181737  0.0181737    0.0181737     0.0181737     0.0181737    …   0.0181737     0.0181737     0.0181737
 0.0181737  0.0181737   11.5379        5.80246       0.00283022       0.00158061    0.00607835    0.0145106
 0.0181737  4.65155      5.93072      11.4036        0.0053046        0.00264009    0.00842839    0.0189501
 0.0181737  2.48606      1.9606        0.0438791     0.000554888      0.000628334   0.000111981  -0.00974379
 0.0181737  1.02964      0.0456341     0.000454459   4.57115e-5       0.000588307   0.000738681   0.00106035
 0.0181737  0.90901      0.000600395   6.45301e-5   -1.19882e-5   …   0.000354857   0.000559608   0.000500321
 0.0181737  0.00121619   9.50736e-5   -3.92466e-5   -3.62156e-5      -0.000212254  -0.000265876  -6.59349e-5
 0.0181737  0.00549957  -1.42342e-5   -2.0833e-5     2.98726e-5       0.000196979   0.000532795   0.00116151
 0.0181737  0.00730426  -3.36528e-5   -1.85244e-6    1.52625e-5       0.000254279   0.00110834    0.00309887

julia> traditional_sol[end,:,:]
9×9 Matrix{Float64}:
 -0.013751  -0.013751   -0.013751     -0.013751     …  -0.013751     -0.013751    -0.013751    -0.013751
 -0.013751  -0.013751    0.0603288    -0.000233445     -0.000608095   0.00147142   0.00508782  -0.0141488
 -0.013751  16.9011     39.415         0.320138         0.00281172    0.00338428  -0.00508294   0.0366225
 -0.013751  17.3233     13.0935        0.0744963        0.0198935     0.0197856   -0.0830545    0.38196
 -0.013751  -0.453438    0.0423686    -0.00234209       0.0201236     0.0255276   -0.976563     1.55339
 -0.013751   8.80398     0.000831992   0.00336582   …   0.0158783     0.0273809    0.108254    -0.326402
 -0.013751  -0.596338    0.00110156    0.00313817      -0.0206732    -0.0179058    0.022136    -0.231748
 -0.013751  -0.0123999   0.000911816   0.00137948      -0.0028375    -0.00512977   0.0182841   -0.0261768
 -0.013751  -0.0154579   0.000448413   0.000278492     -0.00183106    0.0016592    0.0100524   -0.0228178

[cmhyett]

I think this is low risk acceptance that will clear bugs off the backlog for the issymbolic bit. I'd be happy to remedy the tests in another PR if @xtalax agrees with the above assessment.

[ChrisRackauckas]

Okay, because https://github.com/SciML/MethodOfLines.jl/actions/runs/7283474229/job/19847405484?pr=346#step:6:533 scares me a bit, but you're saying it's not the solution interface but the interpolation that's the issue?

[cmhyett]

Yes.

As far as I can tell, this sol.original_sol is the raw output of the ODE solve, but because MoL replaces the boundary values (in this case for periodic BCs), it does not contain boundary information. But as we index into the ODESolution with an oversized grid, (and this is where I get a bit hazy and I'm less confident on what the test is trying to accomplish) I think some backend for ODESolution is trying to perform an interpolation, but it doesn't have the PDE information, so it just returns constants for the boundary values.

As the rest of the tests for the solution interface, and other tests that use the solution interface pass, I'm pretty confident the issue is with the test, rather than the solution interface.

[cmhyett]

Spinning up a PR to get the CI back in shape.

[ChrisRackauckas]

thanks that will be immensely helpful