Report the top error-estimate contributors on solver exit

[ChrisRackauckas-Claude]

Please ignore until reviewed by @ChrisRackauckas.

Motivation

From a Slack thread with @MasonProtter: a large ODE run repeatedly with updated parameters suddenly starts hitting maxiters. Saving every step to see what happened OOMs a 256GB machine, and with save_everystep=false the surviving output is ten time points and a stats block — no NaNs, no large values, nothing to go on.

The solver knew which equation was forcing the step size down. It just never said so. Quoting the thread:

What we want isn't just the EEst, which is the time stepping error estimate, it's EEst = ||atmp||. And EEst > 1 means error too high, reject. What you care about is atmp — because that vector tells you "I have to reject because atmp[i] says the time stepper has too high of an error on equation i".

What this does

Implements SciMLBase.log_error_estimate (added in SciML/SciMLBase.jl#1478) for ODEIntegrator. On any failing exit, the log now carries the scalar estimate plus the top-3 contributing state components:

┌ Warning: Verbosity toggle: max_iters
│  Interrupted. Larger maxiters is needed. [...] Reached t=0.01712924006064487 with dt=3.5068470420252215e-5.
│
│ Error estimate diagnostics:
│ step error estimate EEst = 0.1727 (a step is accepted when EEst <= 1) after 498 accepted and 2 rejected steps
│
│ largest contributors to EEst = internalnorm(atmp), where atmp is the tolerance-weighted local error per state component:
│   atmp[7] = -0.5463, u[7] = 8.311e-07, uprev[7] = 8.311e-07
│   atmp[1] = 2.141e-19, u[1] = 0.9983, uprev[1] = 0.9983
│   atmp[2] = 2.141e-19, u[2] = 0.9983, uprev[2] = 0.9983
└

That is a 10-equation system where only component 7 is stiff — the diagnostic names it, 15 orders of magnitude clear of everything else.

Details:

• atmp is read straight off the cache. Mutable caches keep the residuals after the step, so there is no recomputation and no extra f evaluation; the numbers reported are exactly the ones the controller rejected on.
• Composite and default caches are peeled by cache.current, so the cache that actually ran is the one reported, not the one that would run next.
• Out-of-place caches build the residuals in a local and drop them. Those report the scalar estimate alone rather than guessing.
• Non-finite residuals are counted separately and sort ahead of finite ones, so a single NaN component is named rather than buried.
• Non-adaptive integration returns "" — there is no error estimate to report.
• All of it is behind the exit's verbosity toggle; nothing is computed when the toggle is off.

Printf is added to OrdinaryDiffEqCore for %.4g formatting (also added by #3731; trivial conflict if that lands first).

Tests

test/InterfaceIII/exit_diagnostics.jl covers the unit behavior of top_error_contributors (including the NaN ordering), and asserts through solve that the named component appears for a maxiters exit, an instability exit under both Tsit5 and FBDF, a NaN-producing RHS, and a composite algorithm; that a silent verbosity emits nothing; and that an out-of-place cache degrades to the scalar estimate.

Run locally on Julia 1.11:

Test Summary:          | Pass  Total  Time
top_error_contributors |    4      4  0.1s
Test Summary:                                 | Pass  Total  Time
maxiters names the dominant error contributor |    6      6  1.4s
Test Summary:                                   | Pass  Total  Time
instability exits report the error estimate too |    4      4  1.4s
Test Summary:                       | Pass  Total  Time
non-finite residuals are called out |    3      3  0.3s
Test Summary:                                        | Pass  Total  Time
composite and default caches report the active cache |    2      2  3.2s
Test Summary:                  | Pass  Total  Time
silent verbosity emits nothing |    2      2  1.6s
Test Summary:                                 | Pass  Total  Time
degrades gracefully without a stored residual |    4      4  2.6s
Test Summary:                                            | Pass  Total  Time
non-adaptive integration has no error estimate to report |    1      1  0.3s

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

Depends on SciML/SciMLBase.jl#1478, which defines the log_error_estimate hook and is what makes these diagnostics fire on maxiters at all. CI here will not resolve until that is merged and released — the SciMLBase = "3.41" compat bound points at the unreleased version.

Composes with #3731: that PR's log_numerical_instability reports the Jacobian rows/columns involved, this one reports which components the step controller is choking on, and #1478 makes both run on every failing exit rather than only on dtmin/unstable.

🤖 Generated with Claude Code

https://claude.ai/code/session_01DKB6v14nZHZPYtKiLsPLDT