Fix flaky Weber_BMC2015 gradient check

[FFroehlich]

test_benchmark_gradient[Weber_BMC2015-*-unscaled] has been flip-flopping between passing and failing on Benchmark Collection CPP (3.14, false) -- two runs of the same tree (differing only in CHANGELOG.md, with identical dependency versions) produced one pass and one failure.

The forward and adjoint AMICI gradients agree to nine significant digits, so the gradients are fine; the finite differences are not. The failing direction is a32, where fiddy reports 860.83 against AMICI's 872.68 (1.36%, just over rtol_check=1e-2).

Root cause: fiddy's Consistency checker averages the estimates from every step size whose forward/backward/central differences agree with each other, and Weber has no step size window that suits all directions at once. The noise parameters (e.g. std_yPKDpN25) have such a large second derivative that forward and backward differences only come within 5% of the central one for relative steps <= 5e-5. At those steps the differences for parameters with a small nominal value (a32 ~ 1e-4) are integrator-noise dominated -- the central difference is off by 0.8% at 1e-4 and 4.2% at 1e-5, while being off by only 2e-6 at 2e-1. Those noisy estimates are internally consistent (the bias comes from a shifted solver trajectory, not from per-evaluation jitter), so Consistency accepts and averages them in. Whether a given step size clears the internal agreement check depends on last-ulp details of the runner, which is what makes the outcome vary between runs.

Use central differences only for this problem, over the step size window in which every direction is converged. Measured worst-case relative deviation from the AMICI gradient over {forward, adjoint} x {scaled, unscaled} x {AMICI_EXTRACT_CSE=true, false} drops from 5.5e-3 to 1.9e-3, against an unchanged rtol_check of 1e-2.

method_ids becomes a GradientCheckSettings field, defaulting to the previous forward/backward/central triple, so all other problems are unaffected.

[Copilot]

Pull request overview

This PR stabilizes the PEtab benchmark gradient check for Weber_BMC2015 by avoiding fiddy's cross-scheme “Consistency” averaging behavior in regimes where no single step-size window works across all parameter directions.

Changes:

• Add a method_ids field to GradientCheckSettings (defaulting to the previous forward/backward/central set) so finite-difference schemes are configurable per benchmark problem.
• Override Weber_BMC2015 to use central differences only and restrict step sizes to a converged window.
• Wire method_ids from settings into both benchmark-gradient test entry points.

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[dweindl]

I am trying to address this directly in fiddy (ICB-DCM/fiddy#77).

Waiting for #3223 to collect more data, to confirm the failure mode as I cannot reproduce it locally.

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 77.96%. Comparing base (7772b6d) to head (f919dda).
⚠️ Report is 1 commits behind head on main.

Additional details and impacted files

@@            Coverage Diff             @@
##             main    #3226      +/-   ##
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- Coverage   78.54%   77.96%   -0.59%     
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  Files         318      318              
  Lines       21090    21090              
  Branches     1488     1488              
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- Hits        16566    16442     -124     
- Misses       4516     4640     +124     
  Partials        8        8              

Flag	Coverage Δ
cpp	71.97% <ø> (+0.01%)	⬆️
cpp_python	36.59% <ø> (ø)
petab	48.27% <ø> (ø)
petab_sciml	16.22% <ø> (ø)
petab_sciml_benchmarks	14.78% <ø> (ø)
python	70.34% <ø> (+<0.01%)	⬆️
sbmlsuite-jax	?

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