Fix flaky master CI: relax knife-edge LBFGS objective bound in lotka_volterra test

[ChrisRackauckas-Claude]

Ignore until reviewed by @ChrisRackauckas.

Problem

The master tests / All (julia lts) lane has been failing on the Basic testset (test/lotka_volterra.jl:149):

Basic: Test Failed at test/lotka_volterra.jl:149
  Expression: res2.objective < 0.00015
   Evaluated: 0.00028010684535790533 < 0.00015   # windows lts
   Evaluated: 0.0002385427084901909  < 0.00015   # ubuntu lts

This is the single failing assertion (9 passed, 1 failed, 0 errored, 2 broken).

Root cause: knife-edge threshold on a MaxIters-terminated optimizer

res2 comes from a two-stage UDE training (Adam(1e-3, maxiters=10_000) then LBFGS(maxiters=5000)). The LBFGS stage terminates at MaxIters, not at a gradient tolerance — so the reported objective is whatever value the trajectory happens to reach at the iteration cap. That value depends on BLAS/platform floating-point reassociation, so the assertion flips pass/fail across OSes from run to run:

Run	ubuntu lts	windows lts	macOS lts
2026-06-20	FAIL 2.385e-4	FAIL 2.801e-4	PASS
2026-06-14	PASS	PASS	FAIL 2.705e-4

A converged fit lands anywhere in ~[3.6e-5, 2.8e-4], and the old 1.5e-4 bound sits inside that jitter band. This is benign cross-platform numerical non-determinism, not a regression — the package's structural/gradient/JET tests all pass and the network does train.

Verification (local, Julia 1.10 LTS, linux)

• Full Basic safetestset (test deps resolved via [targets].test): 10 Pass, 2 Broken, 0 Fail (passes locally even with the old 1.5e-4 bound).
• Probe of the exact optimization:
  • DEFAULT_LBFGS res2.objective = 3.583e-5 (retcode MaxIters)
  • Adam-only res.objective = 2.316 (untrained loss is O(1))

So a successful fit is ~4-5 orders of magnitude below the untrained loss, but the exact MaxIters value spans ~10x across platforms.

Fix

Raise the bound 1.5e-4 -> 5e-4 with an explanatory comment. 5e-4 sits safely above the observed jitter band (max observed failing value 2.8e-4, ~1.8x margin) while remaining ~4000x below the untrained O(1) loss, so it still verifies the UDE actually trained without being sensitive to BLAS/platform reassociation. No test is skipped, broken, or silenced; the assertion still fails if training does not occur.

🤖 Generated with Claude Code