PE toroidal torque changes sign under grid refinement while its magnitude stays stable to ~1%

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julia
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hpc

調査の方向性

Start with the reproduction in examples/DIIID-like_ideal_example, then trace how perturbed_equilibrium/energies/toroidal_torque is computed and compare it with the tracked quantity in regression-harness/cases/diiid_n1.toml. Run the stated grid-refinement cases and inspect the torque output in gpec.h5; done means the torque sign is consistent across the reported grids without losing its stable magnitude.

索引モデルが issue の本文から書いたものです。

説明

Summary

perturbed_equilibrium/energies/toroidal_torque on the DIII-D-like ideal example changes sign under small, benign changes to the discretization, while its magnitude stays stable to about 1%. Radial refinement, poloidal refinement, and (independently reported) a dependency update all flip it. A physical torque should not behave this way: the sign is being set by something arbitrary rather than by the physics.

Measured after #350, so the coil-forcing fixes in that PR (b2ec04c3, 8dab0ed9) do not resolve it.

Evidence

All runs use examples/DIIID-like_ideal_example unchanged except for the grid controls named.

Radial refinement on a fixed ldp grid, post-#350 (grid_type="ldp", mpsi as shown; mpsi=0 is the deck's auto grid):

grid torque
auto (561 knots) +0.050865
ldp 512 +0.050892
ldp 1024 −0.050645
ldp 2048 +0.050876

Same scan before #350:

mpsi 128 256 512 1024 2048
torque −0.0507289 −0.0506007 +0.0508128 −0.0510857 +0.0509140

Poloidal refinement at fixed mpsi = 1024 (pre-#350) — changing only mtheta:

mtheta torque
256 −0.0510857
512 +0.0513171

Across every configuration above the magnitude sits in 0.0506–0.0513, a spread of ~1.4%, while the sign takes both values.

It is deterministic, not noise

Re-running mpsi = 1024 and 2048 with the Euler-Lagrange tolerance tightened from 1e-10 to 1e-12 reproduces each value — including its sign — to 1.8e-10 or better:

quantity mpsi el_tol=1e-10 el_tol=1e-12 rel diff
pe_torque 1024 −0.051085748 −0.051085748 4.6e-11
pe_torque 2048 +0.0509139592 +0.0509139592 1.8e-10

So the sign is a reproducible function of the grid, not run-to-run instability, and not integration error.

Independent report of the same symptom

In #338, @matt-pharr reported a set of package updates that "flip the sign of the torque in the d3d ideal example". That is a third, unrelated trigger producing the same signature — sign inverts, magnitude survives.

Why this looks like a convention rather than a convergence problem

A quantity that is converging would show its magnitude settling and its sign fixed. Here the magnitude is already stable to ~1% across an 8× radial refinement, a 2× poloidal refinement, and a code change — while the sign is not stable under any of them. That pattern fits a sign carried by something with an arbitrary choice in it (an eigenvector phase or normalization convention, or a branch selection somewhere in the torque assembly) rather than a physical quantity that has not yet converged.

Worth checking whether the torque is computed from an expression that is genuinely phase-invariant. Quantities built as Im(a* b) are invariant to a global phase on the mode; anything effectively linear in the eigenvector's sign is not.

Why it matters now

The regression harness tracks this quantity (pe_toroidal_torque in regression-harness/cases/diiid_n1.toml, noise_threshold = 1e-12). Any run that lands on the other sign reports a ~200% regression — which is exactly the 200.47% torque "regression" quoted in #338's original table. Until this is resolved the quantity cannot carry a golden value, and it will keep generating false regressions whose cause is invisible to whoever is reading the report.

Reproducing

# in a copy of examples/DIIID-like_ideal_example, set Equilibrium.grid_type="ldp"
# and Equilibrium.mpsi to each of 512, 1024, 2048, then:
julia --project=. -e 'using GeneralizedPerturbedEquilibrium; GeneralizedPerturbedEquilibrium.main(["<deck>"])'
# read perturbed_equilibrium/energies/toroidal_torque from gpec.h5
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