Can MHD turbulence make dust maps good enough to train a CNN?

The goal is a CNN that removes Galactic dust from CMB polarization maps, trained on simulations instead of on the sky itself. This report covers the upstream half: which simulations reproduce the published dust statistics, which ones actually resemble real dust, and what resolution the training maps need.

The paper's Table 1, reproduced with an independent code

finding 1

The paper fits every spectral slope as α = a + b·M_S + c·M_A. We repeated that fit on 100 snapshots streamed from The Well's 256³ boxes, which use the Cho–Lazarian ENO code — unrelated to the paper's Enzo — over its sub-Alfvénic family (M_A ≈ 0.8, M_S from 0.5 to 8.4).

Do simulated maps look like real dust?

finding 2 — revised after review

One estimator, applied identically to simulated maps and to PySM3 dust models at 353 GHz (128×128 patches of 20°, Galactic latitudes 35°–75°, E/B decomposed on the full sphere so nothing leaks at the patch edge, same beam divided out of every spectrum). Simulated maps are whole projected faces binned to 128×128, so that a map wavenumber is a box wavenumber, and the band is k = 3–9 — the range where a 256³ box is still turbulent rather than numerically damped.

Why one 512³ box cost more than the rest of the project

finding 3

We ran Enzo at 512³ at the paper's Planck point on one 112-core node. Parallel efficiency was never the problem: 2.8×10⁵ cell-updates per core per second, 62% of the wall time inside the MHD solver, load imbalance 1.04. The time step was.

The gas itself moves at about 5. The runaway comes from a handful of cells that the turbulence empties to a millionth of the mean density: their magnetic signal speed B/√ρ sets the time step for the whole box, and those cells carry a millionth of the mass and none of the dust emission. Two three-day segments — about 16,000 core-hours — reached 2.44 of the 10 dynamical times requested.

The fix, and the test that it changes nothing

Enzo has an Alfvén-speed limiter that raises the density of exactly those cells until their signal speed reaches a cap. Two details are not in the documentation and came from reading the source: the parameter usually recommended for this (SmallRho) is not a general floor for this solver, and the limiter prints one line per capped cell per step, which at 256³ means gigabytes of log. A one-line patch silences it.

The limiter was then tested rather than assumed: two 64³ runs with identical parameters and forcing seed, one capped and one not.

The two runs are identical to four decimals until the limiter first fires, then drift apart as any two turbulence runs do after a tiny perturbation, so the comparison has to be statistical: no quantity differs by more than its scatter between snapshots. Treating the seven dumps as independent, the 95% intervals on the differences are about [−0.10, +0.84] for α_EE and [−0.52, +0.08] for BB/EE — the test excludes a large effect and nothing finer, from one seed at 64³. The cost reduction, by contrast, is measured directly.

Is 256³ enough to train the CNN?

finding 4

Three measurements on real 256³ data decide this.

Where the turbulence stops being physical

The local slope of the power spectrum is flat through the cascade and steepens where the scheme's numerical dissipation takes over. That knee sits at k ≈ 9 in a 256³ box: physical over a factor of 3 in scale. How far it sits depends on the criterion — between 7 and 14 as the reference window and tolerance are varied — and that spread is part of the result. The common assumption that the knee scales with resolution is not supported by our own ladder: the same criterion gives k ≈ 8 at 64³ and k ≈ 9 at 128³.

What a 128×128 map keeps

Binning a 256² projected face down to 128² costs almost nothing. Cutting a native-resolution quarter tile instead is a mistake, and the reason is the one the review corrected: a half-width tile reaches a given box wavenumber at half its own k, so its band sits at smaller scales, past the knee. Its slopes are steeper by 0.4–0.9 because they are measuring numerical dissipation.

What the same band means on the sky

Planck measures dust over ℓ ≈ 40–600, a factor of 15 in scale. A 256³ box gives a factor of 3. Whether a bigger box buys range in proportion is exactly the scaling our ladder does not support, so the covered range has to be measured per box rather than assumed.

What the external review changed

cross-agent review

A second agent (Codex, OpenAI) reviewed the code and the result files, with a prompt requiring every finding to point at a file, a line or a number. It returned ten findings; eight were accepted outright and two in part. Two were blocking:

The full exchange — prompt, findings verbatim, and a response to each marked fixed, accepted or disputed — is in review/ in the repository. Two earlier attempts produced no review at all: the reviewer's sandbox could not start, and it reported that as a blocking finding rather than inventing results.

What is left