DATASHEET.md

Datasheet — 256³ DNS Turbulence Dataset (turbgen)

Datasheet following Gebru et al. (2021). Every quantitative claim here is grounded in the per-case acceptance appendices (experiments/phase0/results/<case>/DNS_STANDARD_APPENDIX_A.md) and the production catalog; every report carries a provenance stamp (git hash / date / machine / torch version) and full verification tables.

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1. Motivation

• Why was this dataset created? To provide a corpus of 3D incompressible turbulence for training and benchmarking turbulence models, where every configuration is verified against an objective DNS acceptance standard (resolution class, A-group hard gates, and a D-group equation-level consistency check).
• What it adds relative to common practice. Beyond the usual statistics (spectrum, isotropy), each configuration is checked with (a) a D-group verifying the field satisfies the Navier–Stokes equations to time-truncation precision, and (b) high-variance statistics (e.g. A10 isotropy) reported as ensemble mean ± std over an IC-ensemble (multiple initial conditions; see Uses for the honest scope of "independent") rather than a single value.

2. Composition

• Solver: GPU pseudo-spectral DNS of the incompressible Navier–Stokes equations (rotational form), 256³, 2/3-rule dealiasing, Williamson RK3 + Lawson integrating factor for viscosity, fp64 compute. Forcing for steady cases is Eswaran–Pope stochastic Ornstein–Uhlenbeck (random-phase, low-band) — the only forcing that avoids the metastable relaminarization of deterministic band forcing on 256³ (documented negative result, NEGATIVE_RESULT_deterministic_forcing.md).

• Configurations: 15 released frame-configs spanning controlled physics axes (pure-ν Re, forcing-band k_f, correlation-time τ, rotation, passive scalar, stratification, helicity, free decay), plus boundary/validation anchors (NOT released as corpus). All 256³, fp64. The authoritative config list is experiments/phase0/make_splits.py::CONFIGS.

  Released frame-configs (15):

  #	name	axis / type	Re_λ	class	verdict
  #1	ou_relam90	Re axis (k_f=2, τ=2 anchor)	86	I	A+D all-green (14 seeds)
  #2	ou_relam70	Re axis	70	I	A+D all-green (dt=0.05: 16 seeds/2416 fr, A10 cross 1.43%)
  Re50	ou_relam50	Re axis (low end, meas. 54.8)	55	I	A+D all-green (14 seeds)
  kf3	ou_robust_kf3	k_f axis (k_f=3)	73	I	A+D all-green (15 seeds)
  kf4	ou_robust_kf4	k_f axis (k_f=4)	60	I	A+D all-green (16 seeds)
  τ1	ou_robust_tau1	τ axis (τ=1)	80	I	A+D all-green (14 seeds)
  #7	helical_re86	helicity (broken mirror symmetry)	83	I	A+D all-green (13 seeds)
  decay_hotstart	decay_hotstart_re86	free decay (hot start)	86→24	—	decay-criteria + D all-green (8 independent trajectories, v2 2026-07-15)
  decay_saffman	decay_saffman_v2	free decay (initial spectrum p=2)	cold start	—	decay-criteria + D all-green (8 seeds)
  decay_batchelor	decay_batchelor_v2	free decay (initial spectrum p=4)	cold start	—	decay-criteria + D all-green (8 seeds)
  ABC	abc_turb_full	helical decay (Beltrami init)	230→13	—	decay-criteria + D all-green (8 seeds)
  rot-strong	rotating_ro0p2	rotation (Ω=2.5, frac_2D 0.95)	—	I	hard gate (res+D) pass; A10 report-only (8 seeds, cross 0.36%)
  rot-moderate	rotating_ro0p2_v2	rotation (Ω=0.81, frac_2D 0.64)	—	I	hard gate (res+D) pass; A10 report-only (8 seeds, cross 1.41%)
  scalar	scalar_sc1	passive scalar (Sc=1, 5th channel θ)	86	I	hard gate (res+Batchelor+D) pass; A10 report-only (8 seeds, cross 3.31%)
  stratified	stratified_reb40	stratification (Boussinesq, Re_b≈41, 5th channel b)	86	I	complete; hard gate (res+Re_b+Ozmidov+D) pass; A10 report-only (8 seeds, cross 0.42%)

RESOLVED DEFECT (kept for provenance) — decay_hotstart_re86 originally shipped 8 bit-identical copies of one trajectory (verified 2026-07-15: max|diff|=0.0 across all frames, shared ckpt md5, N_eff≈1.0; cause: 8 pools resumed the SAME checkpoint under different seed labels, and corpus_to_zarr.py counted directories). Re-produced same day as v2: 8 genuinely independent trajectories warm-started from 8 DISTINCT ou_relam90 checkpoints (md5 8/8 unique, first-frame pairwise max|diff| ≥ 2.55, DEC-criteria 8/8 green, zarr attrs now carry n_independent_trajectories=8). The defective 79G corpus was deleted with explicit user authorization after v2 passed acceptance. The full record is retained in the production ledger. All 15 configs now have machine-verified independent seeds (benchmark/tests/test_corpus_seed_independence.py, KNOWN_DUPLICATE exemption list now empty).

KNOWN LIMITATION — normalizer constants are transductively fitted. The per-group minmax scalars in each <CASE>_norm_minmax.json were fitted over EVERY frame in the corpus, including val/test seeds (corpus_to_zarr.py never filters by seed). The leak is a single per-group global extremum — not per-sample statistics — and was measured to shift the velocity scalar by ~7% on one config. Fix requires refitting + retraining everything; judged not worth it. Papers using this dataset must describe the constants as "corpus-global frozen scales", NOT "train-only".

Boundary / validation anchors (NOT released as corpus — honest boundary evidence):

#	name	role	note
#4	ou_relam100	Class II resolution boundary	Re_λ111; A2/A4 fail (under-resolved); spectrum+low-order+D usable
#A2	ou_relam95_classII	Class II resolution boundary	Re_λ98; A2=99.47% marginal; densifies the Class II degradation curve
tau4	ou_robust_tau4	admitted at config level, DROPPED from release	τ=4 passed config-admission (long-trajectory 4-seed pooled: A13/13 + D-group, k_maxη=1.551 Class I; see ledger1) but was DROPPED from the released frame-set (2026-06-26): only 3/8 seeds reached uniform-100 frames, rejects all A7 stationarity. Released τ axis is 2 points {1,2}.
TG	tg_re1600	Brachet validation anchor	deterministic symmetric decay; not corpus (half of A-group N/A); ε(t) peak matches Brachet

• Corpus (15/15 complete, dt=0.05, 2026-07-13): frame-configs × independent IC-ensemble seeds × 150 frames per seed for forced/extended (decay configs span the active-decay window). Frame cadence = 0.05 T_L (~1 τ_η) (2026-07-08 dt redesign: the old 0.2 T_L cadence decorrelated adjacent frames and degenerated the rollout task; 0.05 T_L makes the adjacent-frame change ~17%, learnable — aligns with JHTDB/The Well/APEBench). Each seed carries its OWN independent OU forcing sequence (ou_seed = config + IC seed), so the ensemble is a fully-independent ensemble — see §5. Per-config released seed/frame counts (sized so the pooled A10 clears threshold; the k_f=2 high-Re cases need more seeds to beat the few-mode uw floor): ou_relam90 12/2427, ou_relam70 16/2416 (A10 cross 1.427%), ou_relam50 8/1200, kf4/kf3 8/1200, tau1 10/1500, helical 8/1200, rotating×2 8/1200, scalar 8/1089, stratified 8/1200, hotstart 8/400, decay-family per decay span. Each frame is a 4-channel (u, v, w, p) fp32 field of shape [4, 256, 256, 256] (scalar/stratified add a 5th channel θ/b). Pressure is solved by the D4-certified operators.pressure_hat. Each frame is instantaneously Class I (per-frame k_maxη≥1.5 gate). Data currently split across the production machines — see DATASET_MANIFEST_dt0.05.md; merged to a single staging root at release.

• Labels / derived quantities: each frame stores its time t and instantaneous k_max_eta. Per-case appendices give the full A/B/D acceptance tables.

3. Collection process

• Each configuration: spin-up to statistical stationarity (or, for decay, warm-start from a matured field), then a sampling window. Acceptance is computed by the audited referee scripts eval_dns_standard.py (A/B) + eval_dynamics_residuals.py (D); the referee scripts themselves pass known-answer target tests (test_eval_acceptance.py, including adversarial cases that must FAIL) before judging data.
• Corpus frames come from a triple gate: per-frame (instantaneous k_maxη≥1.5), per-trajectory (class/A2/A12/A14/D1–D4), and multi-seed pooling (A10/A7 time-averaged items). Only frames from accepted trajectories enter the corpus.

4. Preprocessing / cleaning / labeling

• Compute fp64, store fp32: storing an already-accepted fp64 field as fp32 is verified safe (A12 incompressibility ~1e-13 after the round trip). fp32 compute is NOT used (it has a structural small-scale instability).
• Per-frame resolution filtering: frames whose instantaneous k_maxη<1.5 are dropped. Consequence (declared in manifest): the dropped frames are the eps-peak (most intermittent) instants, so the corpus systematically under-samples the strong-dissipation tail; high-order intermittency statistics (derivative flatness/kurtosis) are a lower bound, not unbiased. Mild at Re_λ≈86 (dropped eps ~1.3–1.4× the mean). Frames are therefore NOT uniformly spaced in time — loaders MUST use each frame's stored t.

5. Uses

• Recommended: training/benchmarking turbulence foundation models on resolved 3D incompressible turbulence; testing equation-level consistency (D-group); studying forced-steady vs free-decay and non-helical vs helical regimes.
• Use with care / not recommended:
  • Do NOT treat the corpus as an unbiased sample of extreme dissipation events (see §4).
  • Do NOT cite the free-decay decay-rate α as a quantitative physical result: α is a report-only item — it depends strongly on the virtual-origin t0 (a free fit parameter; in-window t0 shifts move α across ~1.3–2.0 at R²>0.998) and deviates from textbook Saffman/Batchelor values. The decay cases' defensible value is the D-group (equation-level correctness), not α.
  • Do NOT judge isotropy (A10) from a single realization: A10 cross-term is a high-variance statistic (per-seed scatter ~0.7–6%); the verdict uses the multi-seed pooled value (corpus: cross 1.92%, comp 2.27%) and is reported as ensemble mean ± std (corpus per-seed cross 2.83% ± 1.39%). This pooling is the DNS standard's own A9/reporting rule ("average ≥5 T_E or ≥8 independent ensemble samples; judge on the mean, report uncertainty"; Pope 2000) — pooling reduces the finite-volume statistical noise of an estimate of a quantity that is ~0 by isotropy, it does not "wash" an anisotropic field isotropic (a truly anisotropic field's pooled value would not drop). All healthy seeds are kept (only laminarized / A14-aborted runs are excluded), thresholds are unchanged, and per-seed scatter is reported alongside the pooled value.
  • Independence of ensemble seeds: each seed varies BOTH the initial condition (--seed) AND the OU forcing sequence — ou_seed = config + IC seed gives every seed its own independent stochastic forcing drive (--ou-seed-per-ic). So the ensemble is a fully-independent ensemble, not merely IC-varied. This is the core of the A10 fix: independent forcing randomizes the sign of the cross-correlations ⟨u_i u_j⟩ across seeds, so signed pooling cancels them to the isotropic value. (An earlier release shared one fixed ou_seed across seeds; that imprinted a common directional bias that signed pooling could not cancel — corrected to per-seed forcing.)
  • #4 (Re_λ111) is Class II: gradient/high-order statistics are N/A (under-resolved); spectrum, low-order moments, and D-group are usable. It is a measured point on the 256³ Class I boundary: the publishable-Re ceiling (~Re_λ 86–90) is not a chosen limit but the objective consequence of the DNS resolution requirement — at fixed N=256 the Class I red line k_maxη≥1.5 caps Re, and #4 (Re111, A2 dissipation-fraction fails) plus ou_relam95 (Re98, A2 marginally fails) are where that line measurably sits. Higher Re is physically reachable only as Class II (spectrum + low-order + D usable, gradients N/A).

6. Distribution

• Format: zarr only (lossless zstd) — .pt frames are an intermediate, deleted after conversion + QA. corpus/<case>/<case>.zarr holds u[N,3,256,256,256] + p[N,256,256,256] (+ θ or b as a 5th field for scalar/stratified) + t/seed/k_max_eta arrays (1 frame/chunk). Storage root is the TURBGEN_DATA_DIR env var (not a hardcoded path), so the tooling is cross-platform. Frozen JOINT-velocity normalizers in <case>_norm_minmax.json (maps to [-1,1]) and <case>_norm_standardize.json (z-score, UNBOUNDED ~±5, pressure to ~−11); velocity is normalized by ONE shared scale (not per-component) to preserve A10 isotropy. Lossless verified bit-exact (random frame spot-checks). seed index orders seeds numerically.
• Hosting: full corpus on Zenodo (DOI), core subset on HuggingFace; data CC-BY-4.0, code MIT.
• License / public release: pending user decision (publication and public release require maintainer sign-off).

Reproducibility scope (honest)

• Bit-exact regeneration requires the ORIGINAL (device, torch version). The OU forcing's random sequence is generated on-GPU; GPU RNG differs from CPU and can differ across GPU architectures / torch versions. The two production machines run different torch (2.11 vs 2.7), so a trajectory is byte-identical only when re-run on the same hardware+torch that produced it. The released fp32 zarr is the canonical bit-exact artifact.
• From the public solver + config + seed + git hash you can regenerate the same flow STATISTICS (spectra, A/B/D-group verdicts) on any fp64-capable device — the dataset's statistical properties are reproducible everywhere; per-byte identity is hardware-bound. This is the standard situation for GPU-RNG DNS and is stated so reviewers reproducing on different hardware expect matching statistics, not matching bytes.

7. Maintenance

• Paper: https://arxiv.org/abs/2608.04222

• Maintainer / contact: Yilong Dai (ydai17@ua.edu). Errata and additions are released as new dataset versions under the concept DOI (10.5281/zenodo.21589489); issues and questions go to the GitHub tracker (https://github.com/Dyloong1/TIDE-dataset-benchmark/issues).

• Two-machine generation (Windows/torch 2.11 and Linux/torch 2.7) sharing one git repo; the solver is cross-machine reproduced (#1 independently reproduced on both OS / torch versions, A+D all-green, consistent). Acceptance appendices carry provenance stamps for traceability.

8. Known limitations / open items

• Production scope: 15 frame-configs × 8–16 IC-seeds (forced) or 8 (ext/decay) × 150 frames (decay configs span the active-decay window, frozen tail excluded), zarr-only. As of 2026-07-13 production is 15/15 complete (all forced/ext/decay accepted and on disk). Per-config accepted-seed counts vary with the per-trajectory gate and the pooled-A10 requirement (forced k_f=2 high-Re cases pool more seeds: relam90 12, relam70 16; others 8–10 — see the released-frame-set table §2 and DATASET_MANIFEST_dt0.05.md). Data is split across the production machines; merged to a single staging root at release.
• Regime framing is honest, not orthogonal axes: only the pure-ν Re axis {Re_λ 55,70,86} is single-variable (the low point measured Re_λ=54.8, nominal "50"). The k_f {2,3,4} and τ {1,2} variations are physically-distinct forcing regimes but are CONFOUNDED with Re (higher-k injection / longer correlation shift ε → Re); the manifest records each config's MEASURED (Re_λ, k_f, τ, ε). Physical diversity comes from multi-physics breadth + this measured-regime coverage, not a wide clean sweep.
• Frame count after the per-frame gate: the instantaneous k_maxη≥1.5 gate drops some frames (Re86-edge configs like scalar drop ~half on the ε-peak instants); production over-provisions the sampling window so enough frames survive the gate. Frame counts are therefore NOT uniform across seeds (accepted as of 2026-07-04); per-seed kept counts are in the manifest.
• Re_λ≈55 caveat (the Re-axis low point, config ou_relam50): a low-Re / dissipation-dominated regime with essentially no inertial range (B-group is report-only below Re_λ100); included as the Re-axis low endpoint, not as an inertial-range-physics sample. Calibrated 2026-06-25: σ²=0.0555 → Re_λ=54.8, A5 L_box/L=5.35 PASS (the flagged A5 risk did not materialize). Named "50" (nominal), measured 54.8.
• #4 D2 re-measured under the frozen protocol (2026-06-21): mean 1.04e-3 (was 3.96e-3 live-forcing); verdict unchanged. All D2 values now use the frozen protocol.