README.md

metadata

license: other
license_name: mixed-per-dataset
tags:
  - multi-fidelity
  - pde
  - scientific-machine-learning
  - neural-operator
pretty_name: MFFP benchmark (42 datasets, corrected)

MFFP benchmark — 42 datasets (corrected release)

Multi-fidelity field prediction: recover a high-fidelity (fine-grid) PDE solution field from cheap low-fidelity (coarse-grid) fields plus a small condition vector, with few HF samples.

Everything lives under benchmark_42/, split into three collections — core/ (15), ext/ (8), sharp/ (19). Per-dataset statistics are in benchmark_42/MANIFEST.csv; the collection tables and the full revision history are in benchmark_42/README.md.

Relationship to nicksung/mf_field

This repo supersedes the 2026-07-28 release at nicksung/mf_field. It exists as a separate repo only because HF personal repos could not be shared as collaborators; it is the same benchmark, with three defect classes corrected.

Do not mix the two. Seven datasets differ:

dataset	what changed
sharp/allen_cahn_1d	condition vector now encodes the IC (cond dim 3 → 19)
sharp/allen_cahn_2d	IC-encoded (3 → 19); LF–HF corr 0.984 → 0.993
sharp/fisher_kpp_1d	IC-encoded (2 → 18); no longer flagged operator-hard
sharp/fisher_kpp_2d	IC-encoded (2 → 50); LF–HF corr 0.758 → 0.984
sharp/phase_field_crystal_2d	IC-encoded (2 → 18)
core/ifc_heat	fidelity levels re-paired to be nested; corr 0.940 → 0.956
core/ifc_poisson	fidelity levels re-paired to be nested; corr 0.827 → 0.909

The other 35 datasets are byte-identical to the 2026-07-28 release.

Separately, the grid-registration ("half-pixel") defect affected the pre-aligned /fields_hf/res_R copies produced by the sharp-field generator and the fidelity-gap metrics the datasets reported about themselves. Aligned copies were built with a cell-centred coordinate map even for node-sampled solvers, displacing every output pixel by (r-1)/2 HF cells. Raw native-grid arrays were never affected. See benchmark_42/README.md for the full statement.

⚠️ 14 of the 42 datasets are degenerate

They ship, but they are labelled. A degenerate dataset is not broken — it is unsuitable for measuring what this benchmark claims to measure, and a model can post an excellent score on it without doing anything interesting. Every flagged dataset carries a warning at the top of its own README.md; criteria and caveats are in benchmark_42/README.md.

flag	criterion	count
operator_hard	the condition vector barely predicts the field	10
copy_lf_trivial	lifting LF to the HF grid already reproduces HF to < 1% rel-L2, structure included	6
level_dominated	copying LF looks near-perfect, but only because the field is nearly uniform	2
mf_useless	LF carries essentially no information about HF	2

The sharpest cases: ext/kuramoto_sivashinsky_1d has an LF–HF correlation of -0.057, and sharp/kuramoto_sivashinsky_2d is reproduced by copying the coarse field to 0.47%.

level_dominated is worth understanding before trusting any score on this benchmark. sharp/fisher_kpp_2d reads a copy error of 0.0006 -- apparently solved by copying -- but its field only spans [0.79, 1.00], so that number is almost entirely the constant offset, which LF gets for free. Remove each sample's spatial mean and the copy error is 0.0216, 35x larger. sharp/allen_cahn_2d goes 0.0069 -> 0.1465, a 21x gap and 15% structural error. On these two the headline relative-L2 metric mostly measures getting the mean right.

Both flags are reported in MANIFEST.csv as copy_lf_rel_l2 and copy_lf_rel_l2_detrended. Note that operator_hard is diluted by the IC-encoded condition vectors introduced in this release -- see the caveats before excluding anything on that basis alone.

Methodology note

Low fidelity is always a real coarse consistent solve — never a downsampled or noised high-fidelity field. Downsampling injects Gibbs and aliasing artifacts and invalidates the benchmark. Fidelity levels are aligned/nested: the same parameter vector is solved on a coarse and a fine grid, so HF - LF residuals are well defined.

Prefer a metric panel over rel-L2 alone — rel-L2 averages over the smooth bulk and hides blur in thin sharp regions.

Layout

benchmark_42/
  MANIFEST.csv                 per-dataset stats for all 42
  README.md                    collection tables + revision history
  core/<dataset>/              train_l*.npz / test_l*.npz  (x, y)
  ext/<dataset>/               train_l*.npz / test_l*.npz
  sharp/<dataset>/             train_l*.npz / test_l*.npz  + meta.json
  core/ifc_{heat,poisson}/     train/fidelity_<F>/{Xs,ys}.npy + test/fidelity_64/

l1 is the coarsest rung. The two ifc_* datasets use the raw per-fidelity layout rather than npz; everything else uses train_l*.npz / test_l*.npz with keys x (conditions) and y (fields).

Licenses vary per dataset — see each dataset's own README.md.

Changelog

• 2026-08-08 — pfc regenerated (crystalline box) + allen_cahn_2d test trim. sharp/phase_field_crystal_2d: all arrays regenerated from an all-crystalline sampling box (r ∈ [-0.4,-0.3], mean_density ∈ [-0.25,-0.2]; MFFP ADR r3-0002) — the previous box left ~half the samples in the uniform phase with no fidelity gap. Additionally its top rung pair (L2→L3) is documented as spectrally converged (no prediction task; use L1 as the LF input — MFFP ADR r3-0004; see the dataset README). sharp/allen_cahn_2d: test split trimmed 100 → 78 rows (22 task-void rows with no copy-LF gap; MFFP ADR r3-0003; dropped indices in meta.json). Train split unchanged. benchmark_42/MANIFEST.csv recomputed for the pfc row (all other rows byte-identical). Scores computed against the 2026-08-05 revision are not comparable on these two datasets. The previous revision remains available via this repository's git history.