README.md

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