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docs: clarify preconditioner experiment results and timing

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Emily Boudreaux
2026-09-17 17:53:07 -04:00
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experiments/PRECONDITIONER_IMPROVEMENT_2026-09-18.md
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@@ -1,9 +1,9 @@
# Preconditioner improvement: matched frozen Newton systems # Preconditioner improvement: matched frozen Newton systems
This experiment changes preconditioning only. The complete Newton Jacobian, This experiment changes preconditioning only. The complete Newton Jacobian,
normalization, physical residual, mesh, and linear acceptance gate are held fixed. normalization, physical residual, mesh, and linear acceptance gate are held
The date in branch and artifact names is an experiment identifier; provenance fixed. The date in branch and artifact names is an experiment identifier;
files contain the actual UTC execution times. provenance files contain the actual UTC execution times.
## Reproduction and scope ## Reproduction and scope
@@ -15,18 +15,20 @@ Integration branch: `research/preconditioner-benchmarks-20260918`, based on
The experiment workspace is The experiment workspace is
`/Users/tboudreaux/.codex/.chatgpt-projects/g-p-6a6b3f2194ec8191bebcd59075897f1d`. `/Users/tboudreaux/.codex/.chatgpt-projects/g-p-6a6b3f2194ec8191bebcd59075897f1d`.
Evidence is under `diagnostics/preconditioner_improvement_2026-09-18` there. Evidence is stored under `diagnostics/preconditioner_improvement_2026-09-18`
Each campaign retains its clean source commit, build configuration, copied in that workspace. Each campaign retains its clean source commit, build
executable and hash, mesh hash, exact commands, input/output hashes, and logs. configuration, copied executable and hash, mesh hash, exact commands,
Runs are serial, without overlapping builds or FEM jobs during timing. input/output hashes, and logs. Runs are serial, without overlapping builds or
FEM jobs during timing.
Frozen comparisons start FGMRES from zero on the same saved state and right-hand Frozen comparisons start FGMRES from zero on the same saved state and
side. Each role constructs a fresh inverse, including its own specification right-hand side. Each role constructs a fresh inverse, including its own
border responses. The restart length is 160, the initial cap is 200 iterations, specification border responses. The restart length is 160, the initial cap is
and the required relative full-J true defect is 0.03. The independently applied 200 iterations, and the required relative full-J true defect is 0.03. The
full Jacobian decides acceptance; the Krylov recurrence flag alone does not. independently applied full Jacobian decides acceptance; the Krylov recurrence
All accepted/trial state buffers, normalization factors, preparation generation, flag alone does not. All accepted/trial state buffers, normalization factors,
and a deterministic full-J probe must remain unchanged. preparation generation, and a deterministic full-J probe must remain
unchanged.
Costs include inverse construction, normalized binding, Krylov setup, Krylov Costs include inverse construction, normalized binding, Krylov setup, Krylov
solve, and full-J verification. Extra diagnostic applications and artifact I/O solve, and full-J verification. Extra diagnostic applications and artifact I/O
@@ -37,30 +39,32 @@ physical convergence.
## Existing two-way coupling: negative controls ## Existing two-way coupling: negative controls
`screen_v1` uses source `018fc1c`, before the cached cross-action optimization. `screen_v1` uses source `018fc1c`, before the cached cross-action
optimization.
| Saved state | Inverse | Iterations | Full-J relative defect | Complete verified cost (s) | | Saved state | Inverse | Iterations | Full-J relative defect | Complete verified cost (s) |
|---|---|---:|---:|---:| |---|---|---:|---:|---:|
| n=1.5, J=0 plateau | independent | 200 | 0.0590170471860 | 87.9302 | | n = 1.5, J = 0 plateau | independent | 200 | 0.0590170471860 | 87.9302 |
| same | stellar LDU | 200 | 0.0600668598825 | 599.5473 | | same | stellar LDU | 200 | 0.0600668598825 | 599.5473 |
| n=1, J=0.1 plateau | independent | 200 | 0.0826534298794 | 86.9409 | | n = 1, J = 0.1 plateau | independent | 200 | 0.0826534298794 | 86.9409 |
| same | stellar LDU | 200 | 0.0720550396371 | 594.2053 | | same | stellar LDU | 200 | 0.0720550396371 | 594.2053 |
All four miss the 0.03 gate. Stellar LDU spends 6.82–6.83 times the total cost; All four solves fail the 0.03 gate. Stellar LDU incurs 6.82–6.83 times the
it slightly worsens the n=1.5 result and reduces the rotating defect by 12.82%. total cost; it slightly worsens the n = 1.5 result and reduces the rotating
Mean inverse application costs rise from approximately 0.19 s to 2.7 s, while defect by 12.82%. Mean inverse application time rises from approximately 0.19
full-J actions remain approximately 0.23 s. The uncached gravity-to-material s to 2.7 s, while full-J actions remain approximately 0.23 s. The uncached
force column explains the application-cost anomaly. gravity-to-material force column explains the application-cost anomaly.
Poisson contributes 95.53% of the squared n=1.5 baseline defect and 98.28% with Poisson contributes 95.53% of the squared n = 1.5 baseline defect and 98.28%
stellar LDU. For the rotating state those fractions are 85.00% and 98.10%; LDU with stellar LDU. For the rotating state those fractions are 85.00% and
reduces the gradient-row norm by 94.16% but the Poisson norm by only 6.35%. 98.10%; LDU reduces the gradient-row norm by 94.16% but the Poisson norm by
These are global normalized block diagnostics, not proof of an exclusively only 6.35%. These are global normalized block diagnostics, not proof of an
exterior error. No exterior weighting is changed. exclusively exterior error. No exterior weighting is changed.
The independent artifact audit passes 65 provenance checks and 93 checks per The independent artifact audit passes 65 provenance checks and 93 checks per
case. Both saved states and the normalization data exactly match their producer case. Both saved states and the normalization data exactly match their
artifacts. The two independent baselines reproduce the earlier failed solves. producer artifacts. The two independent baselines reproduce the earlier failed
solves.
## Candidate mechanisms ## Candidate mechanisms
@@ -83,103 +87,115 @@ artifacts. The two independent baselines reproduce the earlier failed solves.
## First candidate screen ## First candidate screen
`candidates_v1` uses source `dc8d4b0` and the same n=1.5, J=0 plateau state. `candidates_v1` uses source `dc8d4b0` and the same n = 1.5, J = 0 plateau
Every fresh independent control reproduces relative defect 0.059017047186 at state. Every fresh independent control reproduces relative defect
200 iterations. Complete control costs remain between 87.53 and 88.25 s. 0.059017047186 at 200 iterations. Complete control costs remain between 87.53
and 88.25 s.
| Candidate | Iterations | Full-J relative defect | Gate | Complete verified cost (s) | | Candidate | Iterations | Full-J relative defect | Gate | Complete verified cost (s) |
|---|---:|---:|---|---:| |---|---:|---:|---|---:|
| Cached stellar LDU | 200 | 0.0600668598779 | fail | 117.4845 | | Cached stellar LDU | 200 | 0.0600668598779 | fail | 117.4845 |
| Consistent gravity Schur, k=1, omega=0.5 | 132 | 0.0292091549685 | pass | 72.3981 | | Consistent gravity Schur, k = 1, omega = 0.5 | 132 | 0.0292091549685 | pass | 72.3981 |
| Cached stellar LDU + consistent gravity Schur | 121 | 0.0285619160766 | pass | 84.7104 | | Cached stellar LDU + consistent gravity Schur | 121 | 0.0285619160766 | pass | 84.7104 |
| Nine-mode coupled shape coarse correction | 200 | 0.0668657989082 | fail | 97.0564 | | Nine-mode coupled shape coarse correction | 200 | 0.0668657989082 | fail | 97.0564 |
The cached LDU is 5.1032 times faster than its old execution path at the same At the same iteration cap, the cached LDU reduces total execution time by a
iteration cap, while mean inverse application cost drops 8.0425 times. This is factor of 5.1032 relative to the old path, while mean inverse application time
an execution improvement, not a convergence improvement. Saved inputs and the drops by a factor of 8.0425. This is an execution improvement, not a
full-J probe agree exactly; the final normalized correction changes by only convergence improvement. Saved inputs and the full-J probe agree exactly; the
2.7051e-11 relatively. Both LDU solves fail, and the cached version remains final normalized correction changes by only 2.7051e-11 relatively. Both LDU
34.2% more expensive than the independent control on this state. solves fail, and the cached version remains 34.2% more expensive than the
independent control on this state.
Gravity refinement is the first candidate to cross the original gate. It lowers Gravity refinement is the first candidate to cross the original gate. It
the Poisson-row defect by 55.4% and the gradient-row defect by 15.0%. The squared lowers the Poisson-row defect by 55.4% and the gradient-row defect by 15.0%.
Poisson share drops from 95.53% to 77.59%; surface and hydrostatic defects grow, The squared Poisson share drops from 95.53% to 77.59%; surface and hydrostatic
so the improvement is judged by the verified global norm. Work changes from defects grow, so the improvement is judged by the verified global norm. Work
400 to 396 mass-inverse applications, 200 to 264 AMG Schur applications, and changes from 400 to 396 mass-inverse applications, 200 to 264 AMG Schur
200 to 132 outer inverse applications. The default has not yet passed the same applications, and 200 to 132 outer inverse applications. At this iteration
gate, so dividing its failed 88 s attempt by 72.4 s is not a convergence speedup. cap, the default does not pass the same gate, so dividing its failed 88 s
The combined LDU saves another eleven iterations but is 17% slower overall. attempt by 72.4 s is not a convergence speedup. The combined LDU saves another
eleven iterations relative to gravity refinement alone but takes 17% more time
overall.
The coarse candidate has all nine modes active, minimum overlap lower bound The coarse candidate has all nine modes active, minimum overlap lower bound
0.79465, and no fallback. Its extra construction costs 8.6012 s, including mode 0.79465, and no fallback. Its extra construction costs 8.6012 s, including
completion and eighteen setup Jacobian applications; it stores 28,491,680 bytes mode completion and eighteen setup Jacobian applications; it stores 28,491,680
in persistent vectors. The actual FEM subspace check passes. Nevertheless, its bytes in persistent vectors. The actual FEM subspace check passes.
200-iteration defect worsens by 13.3%. This is a negative numerical result for Nevertheless, its 200-iteration defect worsens by 13.3%. This is a negative
these modes on this state, not evidence about every possible coarse space or numerical result for these modes on this state, not evidence about every
rapidly rotating model. The prototype remains confined to experiments. possible coarse space or rapidly rotating model. The prototype remains
confined to experiments.
## Validation status ## Validation status
The integrated library and experiment driver compile with the repository's The integrated library and experiment driver compile with the repository's
Release/ThinLTO configuration. Source dc8d4b0 passes 20 focused serial test cases Release/ThinLTO configuration. Source `dc8d4b0` passes 20 focused serial test
(441,978 assertions), including FEM equivalence, geometry/discretization refresh, cases (441,978 assertions), including FEM equivalence, geometry/discretization
fixed-work algebra, and coarse inverse tests. Distributed unit and coarse tests refresh, fixed-work algebra, and coarse inverse tests. Distributed unit and
pass on two ranks (13 cases and 213 assertions per rank). coarse tests pass on two ranks (13 cases and 213 assertions per rank).
The broad real-FEM MPI run aborts because the existing METIS partition gives one The broad real-FEM MPI run aborts because the existing METIS partition gives
rank no compactified vacuum element, which the mapped mass constructor requires. one rank no compactified vacuum element, which the mapped mass constructor
The failing log is retained; this campaign does not claim distributed FEM Schur requires. The failing log is retained; this campaign does not claim
validation. See the gravity refinement note for the exact scope and evidence. distributed FEM Schur validation. See the gravity refinement note for the
exact scope and evidence.
The evidence checker passes 22 lightweight tests. Independent reviews of the The evidence checker passes 22 lightweight tests. Independent reviews of the
cached LDU and gravity-only cases validate provenance, state/operator invariants, cached LDU and gravity-only cases validate provenance, state/operator
true gates, and child-work accounting. Reviews are stored outside immutable invariants, true gates, and child-work accounting. Reviews are stored outside
campaign directories. immutable campaign directories.
Source fcb7833 adds owning experiment-only Newton recipes through the existing Source `fcb7833` adds owning experiment-only Newton recipes through the
ADL preparation interface. They use the same concrete prepared inverses as the existing ADL preparation interface. They use the same concrete prepared
frozen benchmark and the existing context refresh/border lifecycle. The driver inverses as the frozen benchmark and the existing context refresh/border
supports default, gravity-Schur, and stellar-LDU recipes for ordinary Newton, lifecycle. The driver supports default, gravity-Schur, and stellar-LDU recipes
positivity, curvature, and positivity-curvature runs. This adds no public for ordinary Newton, positivity, curvature, and positivity-curvature runs.
physics-facing solver API. The updated driver builds successfully at `87569c0`. This adds no public physics-facing solver API. The updated driver builds
successfully at `87569c0`.
## Equal-accuracy confirmation ## Equal-accuracy confirmation
`confirmation_v1` uses source `87569c0`, restart160 and a maximum of600 iterations `confirmation_v1` uses source `87569c0`, a restart length of 160, and a
for both roles. The target remains a freshly verified relative defect of0.03. maximum of 600 iterations for both roles. The target remains a freshly
verified relative defect of 0.03.
| State | Inverse | Iterations | Full-J relative defect | Gate | Complete verified cost (s) | | State | Inverse | Iterations | Full-J relative defect | Gate | Complete verified cost (s) |
|---|---|---:|---:|---|---:| |---|---|---:|---:|---|---:|
| n=1.5, J=0 plateau | independent | 231 | 0.0290033752814 | pass | 100.9943 | | n = 1.5, J = 0 plateau | independent | 231 | 0.0290033752814 | pass | 100.9943 |
| same | gravity Schur k=1, omega=0.5 | 132 | 0.0292091549685 | pass | 72.3727 | | same | gravity Schur k = 1, omega = 0.5 | 132 | 0.0292091549685 | pass | 72.3727 |
| n=1, J=0.1 plateau | independent | 600 | 0.0739197073237 | fail | 257.9399 | | n = 1, J = 0.1 plateau | independent | 600 | 0.0739197073237 | fail | 257.9399 |
| same | gravity Schur k=1, omega=0.5 | 600 | 0.0408505998829 | fail | 321.5918 | | same | gravity Schur k = 1, omega = 0.5 | 600 | 0.0408505998829 | fail | 321.5918 |
The n=1.5 speedup to the same requested accuracy is **1.39548x**, or28.34% less For n = 1.5, the frozen linear solve speedup to the same requested accuracy is
complete cost and42.86% fewer iterations. The candidate repeats its earlier132 **1.39548x**, with 28.34% less complete cost and 42.86% fewer iterations. The
iterations and72.3981s timing closely. Both endpoints overshoot the same stopping candidate repeats its earlier 132 iterations, with timing close to the earlier
threshold slightly; neither tolerance nor the full-J check was relaxed. 72.3981 s. Both endpoints finish slightly below the same stopping threshold;
neither tolerance nor the full-J check was relaxed.
Rotation behaves differently. Refinement reduces the600-step defect by44.74%, Rotation behaves differently. Refinement reduces the 600-step defect by
but costs24.68% more and still fails. The remaining gradient and Poisson defects 44.74%, but costs 24.68% more and still fails the gate. The remaining gradient
contribute0.02664 and0.03018 to the global relative norm. The older rotating LDU and Poisson defects contribute 0.02664 and 0.03018 to the global relative
control reduced the gradient contribution to0.001813 while leaving a large norm. The older rotating LDU control reduced the gradient contribution to
Poisson contribution. This supports one complementary LDU+Schur follow-up; it 0.001813 while leaving a large Poisson contribution. This supports one
neither proves a gradient floor nor permits multiplying the separate gains. complementary LDU+Schur follow-up; it neither proves a gradient floor nor
permits multiplying the separate gains.
All73 provenance and186 case checks pass. The reproducible figure and plotting All 73 provenance checks and 186 case checks pass. The reproducible figure and
provenance are in `confirmation_v1_figures`; reported Krylov histories are shown plotting provenance are in `confirmation_v1_figures`; reported Krylov
separately from independently verified final points. Plotting used an existing histories are shown separately from independently verified final points.
compatible Python environment and installed no dependencies. Plotting used an existing compatible Python environment and installed no
dependencies.
## Easy nonlinear and physical regression ## Easy nonlinear and physical regression
The first two `newton_v1` cases use source `bed1893`, the same n=1, J=0 model with The first two `newton_v1` cases use source `bed1893`, the same n = 1, J = 0
no central-density constraint, positivity strategy, and identical tolerances. model with no central-density constraint, positivity strategy, and identical
Both converge in six accepted full steps, with no repairs or rejections. Initial tolerances. Both converge in six accepted full steps, with no repairs or
physical diagnostics and layout are byte-identical; all linear true gates pass. rejections. Initial physical diagnostics and layout are byte-identical; all
linear true gates pass.
| Measure | Independent | Gravity Schur k=1, omega=0.5 | | Measure | Independent | Gravity Schur k = 1, omega = 0.5 |
|---|---:|---:| |---|---:|---:|
| Total linear iterations | 307 | 258 | | Total linear iterations | 307 | 258 |
| Summed Newton iteration time (s) | 191.068 | 199.375 | | Summed Newton iteration time (s) | 191.068 | 199.375 |
@@ -187,17 +203,17 @@ physical diagnostics and layout are byte-identical; all linear true gates pass.
| Complete diagnostic-run wall time (s) | 251.720 | 261.285 | | Complete diagnostic-run wall time (s) | 251.720 | 261.285 |
| Final nonlinear residual | 1.65157e-13 | 1.05839e-13 | | Final nonlinear residual | 1.65157e-13 | 1.05839e-13 |
Both final residuals are below the shared1.81187e-12 nonlinear target. Fewer Both final residuals are below the shared 1.81187e-12 nonlinear target. Fewer
iterations do not produce an easy-case speedup: Newton time rises4.35% and full iterations do not produce an easy-case speedup: Newton time rises by 4.35% and
run time3.80%. The full run includes physical validation and artifact I/O; it is full run time by 3.80%. The full run includes physical validation and artifact
not presented as pure solver cost. I/O; it is not presented as pure solver cost.
All eight virial errors (four definitions at quadrature14 and18) lie between All eight virial errors (four definitions at quadrature orders 14 and 18) lie
2.61811e-7 and3.73092e-7 for both models, comfortably below1e-5. Maximum endpoint between 2.61811e-7 and 3.73092e-7 for both models, comfortably below 1e-5. The
coefficient difference is2.679e-11; radius difference is3.48e-14. The independent maximum endpoint coefficient difference is 2.679e-11; the radius difference is
paired audit also checks mass, density/enthalpy admissibility and local EOS 3.48e-14. The independent paired audit also checks mass, density/enthalpy
metrics. This preserves the existing physical regression, rather than adding admissibility and local EOS metrics. This preserves the existing physical
independent ESTER validation. regression, rather than adding independent ESTER validation.
The two hard nonlinear cases and the targeted rotating coupling follow-up are The two hard nonlinear cases and the targeted rotating coupling follow-up are
still running or pending. Production defaults remain unchanged: the stronger still running or pending. Production defaults remain unchanged: the stronger