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EQUIL/FFS - IMPROVEMENT - Consistent SFL surface sampling and a core knot-density cap for the EL coefficient splines - #398

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EQUIL/FFS - IMPROVEMENT - Consistent SFL surface sampling and a core knot-density cap for the EL coefficient splines#398
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Summary

Each flux surface was traced independently and then splined on that surface's own solver-chosen abscissae before being resampled onto the common θ grid (DirectEquilibrium.jl). The resample error was therefore uncorrelated between neighbouring surfaces — white noise in ψ that grid refinement amplifies rather than reduces. Neither reltol nor abstol touched it, because it is remap interpolation error, not integration error.

The trace now returns its dense solution, and equilibrium_solver root-solves (Brent, bracketed by the monotone jac-weighted flux integral) for the angle at which the normalised straight-fieldline angle reaches each target node, evaluating there. Every surface is sampled at identical abscissae and the resample error at the output nodes is zero. The arclength tracer returns nothing and keeps the previous path.

Investigated under issue #376.

The headline: the answer stops depending on the grid

Solovev, same commit, only this change differing — the free-boundary energy was not converging before and is now converged to 6 significant figures:

mpsi et[1] develop et[1] this PR EL steps develop EL steps this PR
256 1.959e-02 1.462068e-02 1074 775
512 5.399e-02 1.462087e-02 1558 806
1024 8.890e-02 1.462084e-02 2689 891

develop's et[1] drifts 4.5× across the ladder and is still moving; the plasma energy drifts with it (−10.4049 → −10.3144). With this change both are grid-invariant, and the step count is nearly flat (1.04×, 1.11× per doubling versus 1.45×, 1.73×).

That is the property we want: once the equilibrium splines resolve the equilibrium, adding knots should change neither the answer nor the work.

Regression harness

regress --cases diiid_n1,solovev_n1 --refs develop,local, baseline develop @ 9491f89
(branch is current with origin/develop; 1 ahead, 0 behind).

diiid_n1 — physics moves only in the 3rd–4th digit, cost halves:

quantity develop local diff
total energy Re(et[1]) 8.012318e-01 8.004564e-01 0.10%
plasma energy Re(ep[1]) -1.348486e+00 -1.349677e+00 0.09%
vacuum energy Re(ev[1]) 2.149718e+00 2.150134e+00 0.02%
plasma volume 1.829472e+01 1.829471e+01 0.00%
ODE steps (total) 4572 1974 −56.8%

q0, q95, beta_t, beta_n and the singular-surface locations/count are unchanged to 0.00%.

solovev_n1 — et[1] moves 98%. This is the fix working, not a regression: as the table above shows, the develop value is grid-dependent and non-convergent. Solovev's ν node data sat at ~19% relative white noise under the old resample, so it is the case this change corrects most. et[1] is also a near-cancellation (ep ≈ −10.4, ev ≈ +10.4), so a 7% plasma-energy correction dominates it.

On solovev_n1, q0, q95, the singular-surface count/locations/q-values and mpert are all
exactly unchanged; beta_t/beta_n move 0.02%/0.08%.

Runtime 210.6s → 184.5s.

Kinetic cases — large moves, all of which enter at this PR

regress --cases solovev_kinetic_calculated,solovev_kinetic_ntv,solovev_kinetic_nuzero --refs develop,local. This PR moves the kinetic harness values, some of them dramatically — that is owned here, not hidden:

case quantity develop local diff
kinetic_calculated Re(et[1]) 1.845905 1.799588 2.5%
kinetic_calculated Im(et[1]) −1.421059 −1.309210 7.9%
kinetic_ntv NTV torque (fgar), magnitude ~1.56e-4 N·m ~3.85e-1 N·m ~2500×
kinetic_ntv ψ-quadrature integrand evaluations 840 60 −93%
kinetic_ntv root-area-weighted Re(et[1]) 6.773e-1 1.074e-2 −98%
kinetic_nuzero Im(et[1]) −2.034869 −1.559010 23%
kinetic_nuzero Re(et[1]) 2.245440 2.284431 1.7%

Attribution: the stacked follow-up branches (EL grid cap + certified kinetic grid, knob off) reproduce these local values bit-identically (34/34 tracked quantities unchanged vs this branch's head), so every kinetic delta vs develop enters at this commit — none at the follow-ups.

Interpretation: the old per-surface resample injected ~1e-6-level white-in-ψ geometry error (measured; see the mechanism section), and resonance-dominated kinetic quantities amplify exactly that kind of noise — the Solovev cases are the most sensitive in the suite. The quadrature-cost drop (840 → 60 evaluations for the same tolerance) is direct evidence the develop-side torque integrand carried noise structure the quadrature was chasing. The eigenvalue moves (2–8%, 23% for Im at ν→0) are consistent with the ideal-case finding that develop's Solovev values were grid-dependent while this branch's are grid-convergent.

Second change, folded in from #408: cap the core knot density of the EL coefficient splines

(#408 was folded here on 2026-09-04 — both are grid-side fixes aimed at the same symptom, the cap is a no-op on production auto grids so its measurements only mean anything alongside the step numbers above, and the two were benchmarked as a pair throughout. One file, src/ForceFreeStates/Fourfit.jl.)

Summary

The Euler-Lagrange coefficient splines (fmats/kmats/gmats and the primitives) inherited every knot of the equilibrium grid. A cubic spline's third-derivative jumps at knots scale as (node error)/Δψ³, so the equilibrium's near-axis packing (Δψ ~ 1e-6 at high mpsi) amplifies even tolerance-level node error (~1e-9, measured) into huge C² kinks — and the adaptive integrator's step size becomes slaved to the knot spacing. Measured directly: core jump magnitudes grow ~34× per mpsi doubling, and an (tol/J)^¼ step model reproduces the observed step-count ladder.

The coefficients are near-cylindrical in the core and do not need that packing. This PR builds their splines on a subset of the equilibrium grid with core density capped at Δψ ≥ 0.05·ψ below ψ = 0.1. Node values are unchanged — only interpolation density — which is why the physics moves at the 1e-7–1e-8 level.

Stacked on #398 (route (a), same investigation); diff shows only the cap once #398 lands.

Measured (DIII-D stripped decks, route-(a) base, mpsi 512/1024)

mψ=512 mψ=1024
accepted EL steps 2768 → 2188 4403 → 3034
step growth per doubling — 1.59× → 1.39×
warm run 12.8 → 10.4 s (−19%) —
et[1] relative change 3e-8 3e-8
Riccati Δ′ diagonal (all 5 surfaces) 4e-7 —

Not a tuned hack: the rule's basis and its generalization

Form: near the axis every component is a Frobenius power law in ψ; power laws are scale-free, so log-uniform sampling (Δψ ≥ c·ψ) resolves them at constant relative accuracy. Constant: cubic interpolation of ψ^p on a log-uniform grid errs by ~(p·c)⁴/384, so c = 0.05 resolves even the steepest spectrum component (p = m_max/2 = 11) to ~2e-4 — and the physics responds far below that because the steep components carry vanishing solution amplitude. Region: ends at min(0.1, innermost rational − RATIONAL_RES_RADIUS), and no knot inside a rational's resolution window is ever removed — guards for decks (e.g. higher n) whose rationals reach the core; verified no-ops on every current case.

Cross-equilibrium check (four equilibria, two construction paths, three grid families):

case knots EL steps et[1] change
DIII-D efit, traced, log-family m1024 1025→575 −31% 3e-8
tj_analytic_direct, traced, log-family m1024 1025→575 −35% 1.3e-9
LAR, inversion, packed auto m1024 1025→575 −8% exact to 8 digits
Solovev, traced, ldp m512/m1024 505→468 ~0 ~4.5e-7 abs (3e-5 rel via the ±10.4 → 0.0146 cancellation)

The LAR row is the anti-over-fit witness: clean geometry with no noise to exploit, and the cap is still harmless.

Two properties reviewers should know

  1. No-op on production decks. The two-pass auto grid's core spacing already satisfies the cap — verified: 287 → 287 knots on the DIII-D auto deck, and the full harness (diiid_n1, solovev_n1, diiid_n1_riccati, gal_resistive_diiid) reproduces EQUIL/FFS - IMPROVEMENT - Consistent SFL surface sampling and a core knot-density cap for the EL coefficient splines #398's numbers exactly. The cap engages only on explicitly packed fine grids (large mpsi), which is precisely the issue Performance: Why do large equilibrium splines slow down the code? #376 scenario.
  2. A fixed cap beats general curvature selection — measured, not assumed. Removal-error knot selection (drop any knot whose interpolated value matches within δ for every element of all 12 matrices) was implemented and swept: it reaches the physics plateau only at δ=1e-7 where it keeps 504/513 knots and buys nothing, and breaks et[1]/Δ′ at any δ loose enough to matter. The core knots that are safe to remove fail the interpolation test (real coefficient curvature, but the solution components multiplying them vanish as ψ^|m|/2). Interpolation error is the wrong objective; the fixed mechanism-based cap is the right scope for the ideal path. Record: handoff/issue376/RESULTS.md §22–§23 (experiment branch).

Verification

⚠️ Requires third-party human review before merging — do not merge without an approving review.

Rebased onto develop (349a0c2)

Merged develop on 2026-09-04. The only conflict was Fourfit.jl, where develop's MatrixSplines
refactor now builds an immutable IdealMatrices: the cap logic moved into a named helper,
core_capped_knots(xs, rationals), and the constructor builds on the capped subset. Cap
behaviour is unchanged — only its plumbing follows develop.

Verification after the port: runtests_equil 279/279, runtests_grid_refinement 59/59.
Harness vs develop reproduces the headline effect — diiid_n1 ODE steps 4572 → 1974 (−56.8%),
with energies moving 0.02–0.28% (Re(et[1]) 0.10%) and q0/q95/β/singular-surface locations at 0.00%.

⚠️ Known regression this PR introduces: DIII-D kinetic-calculated EL stepping

Bisected cleanly (same deck, worktrees per commit): the DIII-D kinetic_source="calculated" forward integration takes 223,271 steps on this branch vs 7,972 on develop (FFS wall 1079 s vs 427 s), with physics agreeing to ~0.1% (et[1] 1.005545 vs 1.006441). This PR alone reproduces the full-stack number bit-for-bit; the stacked follow-ups add nothing. The proximate signature is an integrator grind at ψ ≈ 0.0012–0.0015 (median step 9e-9 vs develop's 2e-6); the deep mechanism is unresolved at the h5 level — the kinetic matrices, their spline third-derivative jumps, condition numbers, crit, integration start point, and solution norms are all identical at every stored digit between the two runs (open follow-up: the unstored F-matrix spline / step-control internals). No harness case covers this configuration — a DIII-D kinetic-calculated FFS-only case should be added. The stacked PR #414 (near-axis validity suppression) removes the sensitive region on physics grounds and cures the regression outright (4,246 steps — below develop's own baseline).

Caveat, stated plainly: a three-orders-of-magnitude move in the ntv-case torque means the develop baseline for that tracked value was noise-dominated, and the new value has no independent reference yet. This needs a physics reviewer's judgment, not just the attribution argument. If this PR is accepted, the kinetic harness baselines must be re-pinned on the merge commit.

Tests

  • test/runtests_equil.jl — 279 pass (includes the arclength path; its return-type annotation was updated to match)
  • test/runtests_grid_refinement.jl — pass
  • test/runtests_tj_analytic.jl — pass (exercises tj_analytic_direct, the same code path)

Scope / follow-ups

  • Covers eq_type ∈ {efit, efit_arclength, imas, sol, tj_analytic_direct} — everything reaching equilibrium_solver in DirectEquilibrium.jl.
  • Not covered: InverseEquilibrium.jl (chease / lar / tj_analytic / efit_by_inversion), which does its own two-stage SFL resample. Follow-up.
  • DIII-D retains a deep-core residual (steps still grow 1.59× per mpsi doubling, concentrated in ψ<0.05); under investigation separately, likely tied to the EFIT input's own resolution rather than the trace.

⚠️ Requires third-party human review before merging — do not merge without an approving review.

🤖 Generated with Claude Code

Follow-up verification: Δ′ and wall time (requested in review)

The original evidence used diiid_n1/solovev_n1, which run integrator = "forward" and therefore
do not emit the BVP Δ′ matrix at all. Re-ran the Δ′-tracking cases.

diiid_n1_riccati

quantity develop local diff
delta prime (BVP diagonal) [5 elem] [5 elem] 16.73%
delta prime (raw side-major) [10 elem] [10 elem] 2.35%
edge coil response delta_coil [10 elem] [10 elem] 1.26%
total energy Re(et[1]) 8.037196e-01 8.029430e-01 0.10%
# singular surfaces / psi / q 5 5 OK / 2e-09 / 0.0
ODE steps (total) 1649 1358 −17.7%
Runtime 202.5s 192.8s −4.8%

gal_resistive_diiid — the quantities the tearing/matching path consumes

quantity diff
gal PEST3 Δ diagonal 0.01%
‖gal Δ′ matrix‖ 0.03%
gal D_I per surface 0.00%
gal α per surface 0.00%
‖gal inner-layer Δ‖ 0.00%
‖gal Δ_coil block‖ 0.80%
‖gal match cout‖ 1.38%
gal match residual OK
Runtime 216.8s → 213.6s

Reading the 16.73%

It is one element. Δ′ BVP diagonal across an mpsi ladder on the riccati deck:

mpsi develop this PR
256 [9.7, −1.9, −13.1, 103024, 336.0] [9.7, −1.9, −13.1, 102768, 336.1]
512 [7.2, −5.2, −16.6, −1319.5, 61.4] [7.2, −5.2, −16.6, −1293.2, 61.5]
1024 [8.6, −5.5, −16.1, −2368.8, 55.1] [8.6, −5.5, −16.1, −2368.0, 55.6]
drift vs previous mpsi 174% → 79.5% 174.7% → 83.1%

The 4th entry (q = 5 surface) runs 1e5 → −1319 → −2369 and changes sign: it is not converged in
mpsi on either version, so it cannot discriminate between them. The other four diagonal entries
agree between versions at every grid, and version-to-version agreement on the full diagonal is
0.25% / 2.0% / 0.03% at mpsi 256 / 512 / 1024.

Caveat worth stating plainly: this PR does not improve Δ′ convergence either (drift
174.7%/83.1% versus develop's 174.0%/79.5%). The unconverged q = 5 Δ′ element is a pre-existing
issue that this change neither causes nor fixes, and it deserves separate attention.

Wall time improves on every case measured: forward diiid_n1 210.6 → 184.5 s, diiid_n1_riccati
202.5 → 192.8 s, gal_resistive_diiid 216.8 → 213.6 s.

@logan-nc @claude
EQUIL - IMPROVEMENT - Sample every flux surface at the same straight-…
de0db4f 
…fieldline angles

Each surface was traced independently and then splined on that surface's OWN
solver-chosen abscissae before being resampled onto the common theta grid, so the
resample error was uncorrelated between neighbouring surfaces -- white noise in psi
that grid refinement amplifies rather than reduces. Neither reltol nor abstol touched
it, because it is remap interpolation error rather than integration error.

The trace now returns its dense solution, and equilibrium_solver root-solves (Brent,
bracketed by the monotone jac-weighted flux integral) for the angle at which the
normalised straight-fieldline angle reaches each target node, evaluating there. Every
surface is sampled at identical abscissae and the resample error at the output nodes
is zero. The arclength tracer returns nothing for the solution and keeps the previous
path.

Measured on DIII-D stripped decks at eulerlagrange_tolerance 1e-10, accepted
Euler-Lagrange steps fall 2309/3977/7638 -> 1881/2768/4403 for mpsi 256/512/1024, a
42% reduction at mpsi=1024, and the per-doubling growth drops from 1.92x to 1.59x.
Surface geometry residuals now converge with refinement instead of sitting on a floor,
and every knot-to-knot correlation turns positive.

Co-Authored-By: Claude Opus 5 (1M context) <noreply@anthropic.com>
logan-nc added a commit that referenced this pull request Aug 17, 2026
@logan-nc @claude
FFS - EXPERIMENT - Phase A diagnostics cancel Phase B; route (a) land…
f1ac78a 
…ed as PR #398

The A3 kill-switch fires: route (a) geometry already agrees with a near-exact trace
to 5e-10..2e-8, i.e. at the integration tolerance, so the planned SFL reparametrisation
would fix an error that is not there.

Also records that nstep is hypersensitive -- a 5.3e-11 geometry perturbation moves it
1.2% -- so the leftover 15-20% gaps are not reliable signal; that A1 places the residual
in the traced construction rather than the EFIT input (analytic input, traced 1.47x vs
inversion 1.18x); and that tightening the trace tolerance 1000x on that case is null.

Notes the harness baseline was refreshed from a stale local develop, and that the first
etol test was a no-op because the deck has no etol key.

No src changes on this branch.

Co-Authored-By: Claude Opus 5 (1M context) <noreply@anthropic.com>
logan-nc added a commit that referenced this pull request Aug 17, 2026
@logan-nc @claude
FFS - EXPERIMENT - Verify Delta-prime and wall time for PR #398
720f015 
The original PR evidence used forward-integrator cases, which emit no BVP Delta-prime
at all, so route (a) had never been checked against the observable that section 19
showed can break silently. Ran diiid_n1_riccati and gal_resistive_diiid.

Tearing-consumed quantities are unchanged: PEST3 Delta diagonal 0.01%, Delta-prime
matrix norm 0.03%, inner-layer Delta 0.00%. The headline 16.73% on the raw BVP
diagonal is a single element (q=5) that runs 1e5 -> -1319 -> -2369 and changes sign
across the mpsi ladder on BOTH versions, so it cannot discriminate between them.

Records that route (a) does not improve Delta-prime convergence either, flagging the
unconverged q=5 element as a pre-existing issue worth its own investigation. Wall time
improves on all three cases.

Co-Authored-By: Claude Opus 5 (1M context) <noreply@anthropic.com>
This was referenced Aug 17, 2026
Draft
Merged
logan-nc and others added 2 commits August 18, 2026 08:44
@logan-nc @claude
FFS - IMPROVEMENT - Cap the core knot density of the EL coefficient s…
aefa3cf 
…plines

The Euler-Lagrange coefficient splines inherited every knot of the equilibrium grid.
A cubic spline's third-derivative jumps at knots scale as (node error)/dpsi^3, so the
equilibrium's near-axis packing (dpsi ~ 1e-6) amplifies even tolerance-level node
error into huge C2 kinks, and the adaptive integrator's step size becomes slaved to
the knot spacing -- measured directly: core jump magnitudes grow ~34x per mpsi
doubling while a (tol/J)^(1/4) step model reproduces the observed step-count ladder.

The coefficients are near-cylindrical in the core and do not need that packing. Build
their splines on a subset of the equilibrium grid with core density capped at
dpsi >= 0.05*psi below psi = 0.1; node values are unchanged, only knot density.

Measured on DIII-D stripped decks (route-a base, mpsi 512/1024): accepted EL steps
2768 -> 2188 and 4403 -> 3034, per-doubling growth 1.59x -> 1.39x, warm run -19% at
mpsi=512, with et[1] unchanged to 3e-8 relative and the Riccati BVP Delta-prime
diagonal unchanged to 4e-7 on all five surfaces.

Interim fixed-cap form; a matrix-curvature knot selection is planned to replace the
fixed rule, with this commit as the fallback.

Co-Authored-By: Claude Opus 5 (1M context) <noreply@anthropic.com>
@logan-nc @claude
FFS - MINOR - Log the coefficient-spline grid only when the cap remov…
a737b3d 
…es knots

On the production two-pass auto grid the cap is a no-op (its core spacing already
satisfies the density rule), so the unconditional message was noise.

Co-Authored-By: Claude Opus 5 (1M context) <noreply@anthropic.com>
@logan-nc logan-nc mentioned this pull request Aug 18, 2026
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logan-nc commented Aug 18, 2026

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Report with visuals for workflow and results can be found here: https://claude.ai/code/artifact/873c8376-3f75-4fe4-934b-4d39f23e2376

@logan-nc @claude
FFS - IMPROVEMENT - Ground the density cap in the Frobenius scale and…
0c17097 
… protect rationals

Reframes the cap as log-uniform sampling of the Frobenius region: near the axis every
component is a power law in psi, and cubic interpolation of psi^p on a log-uniform
grid errs by ~(p*c)^4/384, so c = 0.05 resolves even the steepest spectrum component
(p = mmax/2) to ~2e-4 while the physics responds far below that.

Two generalization guards, motivated by cross-equilibrium testing: the capped region
now ends at the innermost rational surface when that sits inside psi = 0.1, and no
knot inside a rational's RATIONAL_RES_RADIUS window is ever removed -- preserving the
Delta'-stencil structure for decks (e.g. higher n) whose rationals reach the core.
Both guards are no-ops on every current case, verified: DIII-D m512 and Solovev m512
reproduce the previous cap's step counts and knot sets exactly.

Cross-equilibrium check of the rule itself: tj_analytic_direct m1024 (analytic,
traced) 1470 -> 959 steps at et[1] 1.3e-9; LAR m1024 (inversion path, clean geometry)
951 -> 875 at et[1] identical to 8 digits; Solovev ldp m512/m1024 ~unchanged steps at
~4.5e-7 absolute et[1] shift (a +-10.4 cancellation amplifies this to 3e-5 relative).

Co-Authored-By: Claude Opus 5 (1M context) <noreply@anthropic.com>
@logan-nc

logan-nc commented Aug 19, 2026

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Review package (visual companion to this PR — mechanism diagram, the Solovev et[1] grid-convergence before/after, step ladders, geometry-residual evidence, and the Δ′ referee table):

📦 https://claude.ai/code/artifact/873c8376-3f75-4fe4-934b-4d39f23e2376

Self-contained page; complements rather than duplicates the description and diff. If the link does not resolve, ask @logan-nc to enable sharing on it.

@logan-nc logan-nc mentioned this pull request Aug 19, 2026
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@logan-nc @claude
FFS - EXPERIMENT - Kinetic harness attribution: branch is bit-neutral…
83b2a52 
… vs #398; deltas inherited

Co-Authored-By: Claude Opus 5 (1M context) <noreply@anthropic.com>
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This pull request is missing an assignee and a reviewer.

If you are not ready to name them, mark this pull request as a draft.
docs/development/contributors.md suggests lead developers to ask.
Merging is not blocked here, but no pull request may be merged without human review.

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@logan-nc @claude
EXP - DOC - s30: develop baseline exonerates the kinetic model; the D…
a203596 
…III-D step explosion is a #398 regression

Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01LzbLFQKyuRE5DYZmLokKmk
@logan-nc logan-nc mentioned this pull request Aug 21, 2026
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@logan-nc logan-nc changed the title EQUIL - IMPROVEMENT - Sample every flux surface at the same straight-fieldline angles EQUIL/FFS - IMPROVEMENT - Consistent SFL surface sampling and a core knot-density cap for the EL coefficient splines Sep 4, 2026
logan-nc added a commit that referenced this pull request Sep 4, 2026
@logan-nc @claude
Merge develop (via #398) into feature/kinetic-axis-validity
2321a49 
Port the kinetic guards onto develop's structures rather than fighting the reorg:

- MatrixSplines replaces FourFitVars: kinetic matrices read mats.ideal and return
  a fresh MatrixSplines, so the ideal-restore workaround is gone (develop's
  _compute_fkg_matrices is idempotent by construction).
- Arbitrary-psi kernel evaluation returns as a type-stable psis::Vector{Float64}
  (empty = metric.xs), no Union sentinel.
- Multi-ion: the near-axis boundary is now the widest-orbit species' psi_c.
- Sub-threshold cond(F-bar) reporting follows find_kinetic_singular_surfaces!
  into Surfaces/Finding.jl.
- main keeps develop's shape: resonance pinning, the validity boundary, the
  regularization policy and the Validity output move into named helpers in the
  owning modules (KineticForces.resonance_grid_nodes / axis_validity_boundary /
  write_validity!, and kinetic_regularization_kwargs beside perturbed_equilibrium).

Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01LzbLFQKyuRE5DYZmLokKmk
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