MeanField/experiments/KRYLOV_HYPOTHESIS_2026-09-16.md

Krylov correction safeguard: observed outcome

Retain the true-residual initial-guess safeguard as a limited inner-solver robustness improvement. The matched n=1 solution is unchanged, and the capped n=1.5 run uses fewer linear iterations and avoids its control's late linear failure. It does not resolve the n=1.5 nonlinear plateau or establish full physical validation.

Tested guard revision: 1911a26a9a283eed7e53b03fc3481ee894e61bfb. Matched control revision: 9bd4af699650e2a6bbe795c618e6ef3fbcb48e12. The underlying numerical snapshot is 80cc3d8; the safeguard implementation is ed75830. Both live comparisons use restart 160, omit the central constraint, allow eight Newton attempts and 200 linear iterations, and require a true linear residual/RHS <=0.03. Newton stopping uses atol=0 and rtol=1e-8.

The production candidate safeguards a supplied linear initial guess using its true residual under the current operator. It retains the guess when ||b-Jp_guess|| <= ||b||, otherwise starts at zero. A nonzero guess costs one extra operator action, included in reported counts and solve time. Zero guesses do not incur an extra action. This is neither Krylov basis recycling nor a guarantee of fewer iterations: a smaller initial residual can still excite a harder set of modes.

The retained (1-alpha)p heuristic from damped Newton remains intact, as does the existing backend API. The safeguard only declines a guess that increases the current true defect. It also handles a nonfinite operator action on an otherwise finite guess by choosing the finite zero guess, collectively across the communicator. Existing input checks still reject nonfinite supplied vectors. There is no public API or policy-option change, and no change to physical specifications, normalization, preconditioner, tolerances or nonlinear acceptance. The reported initial residual belongs to the effective guess after safeguarding; it does not expose the raw residual of a discarded guess.

Matched live evidence

At n=1, J=0.05, both runs converge in seven full steps and 292 linear iterations to F=3.38036278e-11. Saved state, initial/final physical tables, layout, block residuals and trial histories are byte-identical. Every non-time Newton history field also matches. All eight q14/q18 energy/force virials with P(h) and P(rho) pass 1e-5; the largest is 3.73465327e-7. Full steps leave zero guesses, so this is a regression control, not evidence that the safeguard accelerates cold solves.

At n=1.5, J=0, initial physical tables and the first two numerical histories match exactly, including block records through the third attempt's before-state. The first reset then changes the effective initial defect/RHS from the control's 1.50970280 to 1, and reduces linear iterations from 71 to 65. Both accept alpha=1/64 after four trials. Resulting F is 1.75410130e-4 guarded versus 1.75953185e-4 control. Later trajectories differ; their discarded raw guesses cannot be inferred from the effective initial-residual reports.

Capped n=1.5 outcome	Control	Guard
Accepted Newton steps	7	8
Termination	Eighth linear solve fails	Newton iteration cap
Final F	1.75134755e-4	1.74946086e-4
Last accepted alpha	1/2048	1/8192
Total linear iterations	672	561
First seven attempts' linear iterations	472	467
Sum of linear solve times	303.52 s	242.92 s
Sum of Newton-attempt times	487.15 s	447.25 s
Process time, including diagnostics	550.36 s	508.16 s

The guard passes every linear gate within this cap; the last true residual/RHS is 0.02995827. Most of the total iteration reduction comes from avoiding the last 200-iteration failure. The seventh guarded solve costs 94 iterations versus 80 in the control, so improvements are not uniform. These are different later linear systems and single timings, not a same-matrix or reproducible speedup measurement. The inactive n=1 control itself varied by approximately 5% in time.

Both n=1.5 endpoints remain unconverged and have similar unresolved local errors. Guarded q18 P(h) energy/force virial errors are 2.24342463e-6 / 2.35159576e-6; changes from control are +9.04e-9 / +2.02e-8. The q14/q18 difference is 1.84e-9. Full P(rho) virials remain undefined from sampled DG density negativity. The negative-density mass fraction changes only from 2.89327559e-5 to 2.89305795e-5; no negative enthalpy is sampled. Peak/RMS EOS and Bernoulli errors improve slightly. Mass error increases from 3.50011e-6 to 3.52971e-6. Center-of-mass displacement worsens from 1.67437e-6 to 4.57477e-6 of the unit reference radius and remains an explicit follow-up metric. Sampled signs and extrema are not pointwise bounds.

The standalone solver-and-virial checker passes n=1 and fails n=1.5, preserving strict stopping and pressure-validity distinctions. P(h) virial success alone does not validate the interior. Severe damping first occurs with a cold guess on the second n=1.5 attempt, so adverse warm starts cannot be the entire cause.

Regression checks and reproduction

All five unique focused tests pass on one MPI rank: two backend tests with 41 assertions and three Newton integration tests with 356243 assertions (356284 total). Both backend tests also pass on two MPI ranks, with 41 assertions on each rank. Coverage includes beneficial-guess retention, restart/reporting, rank-0-only adverse guesses, finite coefficients whose operator action overflows, collective fallback, and the existing Newton correction-reuse integration.

The exact filters are [solver][linear][fgmres][warm-start] and [solver][newton][warm-start],[solver][newton][fgmres], with Catch RNG seed 20260916. Only the backend filter is used in the two-rank check. Test binary SHA-256: 258f749ce85e14136b8f7a5fe28e3a49f8007c6bfe37fedd81e27119a8be1d23.

Reproduce guarded live cases with run_plateau_campaign.py and plateau_krylov_cases.json; compare the corresponding restart-160 cases in plateau_control_cases.json at the control revision. Mesh SHA-256: ce11ae99e21e6c3bbfbee402acd2e191c1da0d8261d2227b4203f73f2f337a74. Guard executable SHA-256: a16dfd624e74e89a0b6f78d0cd3742e58274b09580f09b3583d3a37fa4004d46.

Raw runs, exact commands, logs, copied binaries, hashes and full analysis are retained outside git under the campaign's controls/, guard/, guard_checks/ and guard_analysis.md. Recorded CMake caches are identical. Dynamic libraries are not frozen and inherited thread settings are not captured. Direct frozen MFEM probes bypass this production safeguard and cannot validate its behavior.