From d82540a13c4245cc2fc02233a13154da1b112b8b Mon Sep 17 00:00:00 2001 From: Emily Boudreaux Date: Fri, 18 Sep 2026 08:14:07 -0400 Subject: [PATCH] Record preconditioner conclusions and define next nonlinear obstruction investigation --- ...NONLINEAR_STEP_INVESTIGATION_2026-09-18.md | 111 ++++++++++++++++++ 1 file changed, 111 insertions(+) create mode 100644 experiments/NONLINEAR_STEP_INVESTIGATION_2026-09-18.md diff --git a/experiments/NONLINEAR_STEP_INVESTIGATION_2026-09-18.md b/experiments/NONLINEAR_STEP_INVESTIGATION_2026-09-18.md new file mode 100644 index 0000000..3715e78 --- /dev/null +++ b/experiments/NONLINEAR_STEP_INVESTIGATION_2026-09-18.md @@ -0,0 +1,111 @@ +# Nonlinear step obstruction after gravity preconditioning + +## Recorded decision from the completed preconditioner investigation + +The completed report is `PRECONDITIONER_IMPROVEMENT_2026-09-18.md`, committed +at `dc1da62` on `research/preconditioner-benchmarks-20260918`. Its immutable +campaigns live under the task workspace's +`diagnostics/preconditioner_improvement_2026-09-18/` directory. + +- Consistent gravity Schur refinement solves the saved n = 1.5, J = 0 linear + system in 132 iterations and 72.3727 s, versus 231 iterations and 100.9943 s + for the independent control. Both satisfy the same independently verified + relative full-J defect of 0.03: a measured 1.39548x speedup. +- Combining this refinement with stellar LDU solves the saved rotating + n = 1, J = 0.1 system in 142 iterations and 96.8236 s. The independent and + gravity-only controls still fail after 600 iterations. Their finite + time-to-convergence is unknown, so no rotating speedup ratio is reported. +- Prepared geometry reuse makes the existing stellar LDU application 8.0425x + cheaper without improving its convergence by itself. Retain this + implementation optimization independently of policy selection. +- The tested nine-mode shape correction does not improve the n = 1.5 case. + It remains an experimental negative result, not a rejection of all coarse + spaces. +- The easy n = 1, J = 0 model preserves all eight virials below 3.74e-7, + while the stronger inverse costs about 4% more. Defaults remain unchanged. +- Neither hard nonlinear model is physically acceptable. Negative sampled + density makes density-pressure virials undefined. In rotation, a smaller + nonlinear residual accompanied a larger enthalpy-pressure virial error. + Residual decrease is not a substitute for virial and field-admissibility + validation. No angular momentum has been calibrated to critical rotation. + +## New investigation and controls + +Branch: `research/nonlinear-step-obstruction-20260918`, based on `dc1da62`. +The configured worktree is reused to avoid an unrelated full rebuild; the +preceding branch and copied campaign executables retain their exact source +and binary identities. This branch adds experimental diagnostics only. + +Start with the n = 1.5, J = 0 endpoint of +`newton_v1/n1p5_J0_curvature_gravity_schur`. All twelve outer linear solves and +all 31 auxiliary gravity solves passed, but the final nonlinear residual was +1.3966991e-5 against a target of 2.7365922e-12. The final accepted alpha was +1/512. Every trial prepared successfully; all nineteen rejections were +residual-decrease failures, and geometry never limited the step. + +The final squared-residual shares are approximately 42.42% hydrostatic, +26.23% closure, 15.87% surface, 10.43% gravity, and 5.05% mass. This motivates +examining retained-equation curvature after the gravity correction, rather +than assuming the earlier gravity or pressure-preparation failure persists. + +Keep the complete physical equations, fixed normalization, optional +central-density specification (absent here), mesh, and acceptance thresholds +unchanged. Use one gravity Schur refinement at relaxation 0.5 and the same +restart length 160. Fresh cold solves and independently applied full-J true +defects determine direction quality. Trial probes never commit a model. + +## Questions and discriminating evidence + +1. **Does the prepared trial path have the expected tangent?** For frozen + residual F and computed direction p, measure Jp and actual prepared + differences. The curvature-corrected path should preserve that tangent + because its gravity correction is second order in alpha. A discrepancy + that remains first order above arithmetic noise would implicate the + linearization or preparation path. +2. **Does the inexact linear direction cause the obstruction?** Compare + directions at the same saved state with forcing tolerances 0.03 and 0.003, + subject to a recorded finite iteration budget. A tighter requested + tolerance counts only if its independent true gate passes. Failed solves + are recorded and do not substantiate this comparison. +3. **Which nonlinear terms oppose the linear prediction?** Split p into its + actual surface coordinates and all remaining coordinates. Compare raw + and gravity-corrected trials for full, shape-only and fields-only + directions. Form mixed remainders by vector subtraction. Signed + projections against the full linear prediction distinguish adverse + curvature from large but cancelling terms. +4. **Is the behavior specific to the late state?** Use the same-polytrope + Lane–Emden seed as an early-state control, where the previous production + run accepted its first full Newton step. Record preparation and enthalpy + feasibility separately from the residual metric. + +For phi = ||F||^2/2 and ||Jp + F|| <= eta ||F||, + + phi'(0) = <= -(1-eta) ||F||^2. + +At eta = 0.03 the slope must be strongly negative if J differentiates the +prepared path. The production sufficient-decrease test therefore ought to +accept sufficiently small resolved steps. The investigation measures whether +large adverse higher-order terms explain how small those steps become. + +Each block's vector remainder R = F_trial - F - alpha Jp must satisfy + + ||F_trial||^2 = ||F + alpha Jp||^2 + + 2 + ||R||^2. + +For the corrected trial map, its mixed remainder includes interactions +introduced by gravity correction; it is not identified solely with the raw +physical shape Hessian. Below-floor differences are unresolved, not evidence +of exact linearity. + +## Execution and validation + +Run a late-state probe first, then use its evidence to choose the matched +tighter-direction and early-state controls. All model jobs and builds run +serially. The campaign runner records clean source commits, exact commands, +input/output and executable hashes, and refuses existing output directories. +The diagnostic saves the frozen vectors, layout and normalization, checks +restoration and accepted-buffer invariance, and reports failed preparations +and inner solves without inventing values for missing trials. + +Results are pending. No numerical remedy or new convergence claim follows +from the investigation design alone.