NurshatMenglik/NeuralConvection_2D_TrainTest

NeuralConvection — 2D Training/Test Data (version 2)

📄 Paper: A Neural Surrogate Approach for Simulating Natural Convection Problems (arXiv:2606.25259) — Nurshat Menglik, Alex Shao, David Hyde.

Version 2 (September 2026) replaces the original release. All pairs were regenerated; see What changed in version 2. The original tensors remain available unchanged under the tag v1.0-legacy (snapshot_download(..., revision="v1.0-legacy")). New work should use version 2.

Paired 2D Boussinesq → compressible steady natural-convection fields in the unit square, used to train and evaluate the 2D Fourier Neural Operator (FNO) surrogate of the paper. Each pair solves the same randomized problem with both models on the same 64 × 64 mesh.

Each split provides

• X.pt — Boussinesq input, shape (N, 4, 64, 64), float32
• Y.pt — compressible target, same shape
• kept_samples.txt, per_sample.csv, MANIFEST.json — sample ids, per-sample parameters (Ra, Ma, wall dials, pressure de-ramping coefficients, input-vs-target differences) and the packing conventions

Channels of both tensors: [u_x, u_y, T, p] on a uniform 64 × 64 grid; row index = y (row 0 at the bottom), column index = x (column 0 at the hot wall); gravity points along −y.

Splits

Folder	N	Description
train/	4,000	Stochastic Fourier wall temperatures (per-wall complexity dials; adiabatic top/bottom walls possible)
train_legacy/	5,000	Constant hot left / cold right wall, adiabatic top and bottom (the classical cavity)
test_in_distribution/	200	Same generator as train/, independent seed stream
test_ood/	200	Same generator with the vertical-wall dial drawn from {4,5,6} (3–5 Fourier modes per side wall) against {1,2,3} in train/; horizontal walls, amplitude band and Ra law as in train/. The out-of-distribution set of the paper (Test Set 3); no constant-wall samples can occur
test_rand_shift/	200	Same generator with the admissible wall-amplitude band halved: a covariate shift inside the training support. Kept for the record; no longer used in the paper, which uses test_ood/ as its third 2D test set
test_legacy/	200	Classical cavity, independent seed stream

Ra is log-uniform in [1e2, 3e6] (capped at 2e6 when a horizontal wall is conducting), Pr = 0.71, wall temperatures in [0.4, 1.6] (T_init = 1, ΔT = 1.2). The six seed streams are disjoint, so no problem appears in two splits. train/flagged_samples.json lists two training pairs whose Rayleigh number was lowered because the canonical draw did not reach a steady state.

Note: test_in_distribution/ shares its seed stream with the res-32 block of the 10,000-sample release (its first 200 samples are the same problems at 32 × 32); do not train on that block if you evaluate on this split.

Units and conventions

• Both members are in one unit system, the buoyancy (free-fall) scales used by the compressible model: velocity in U = sqrt(gβΔT·L), pressure in ρ₀U², temperature as T/T₀. The Boussinesq model is non-dimensionalized with this same velocity scale (its coefficients are sqrt(Pr/Ra), 1 and 1/sqrt(Ra·Pr) instead of the Pr, Pr·Ra, 1 of the thermal-diffusion convention), so no unit change is applied to either member and the pair differs by physics only. To recover the thermal-diffusion (de Vahl Davis) convention multiply velocities by sqrt(Ra·Pr) and pressures by Ra·Pr (sqrt_RaPr in per_sample.csv).
• Pressure is the solver's raw pressure with its spatial mean and its linear-in-y hydrostatic component removed, for both members (a_B, b_B, a_c, b_c in per_sample.csv are the removed fits); the Boussinesq pressure is stored with the sign convention of the compressible one.
• Values are not normalized. The models in the paper use a per-sample, per-channel affine map taken from the min–max range of the sample's own input X and applied identically to X and Y.
• Both members are marched to a steady state (per-step relative change below 1e-6).

What changed in version 2

1. Boussinesq buoyancy term. Version 1 assembled the Boussinesq body force with T/T_init instead of (T − T_init)/ΔT; with ΔT = 1.2 that is an effective Rayleigh number of 1.2·Ra for the Boussinesq member while the compressible member ran at Ra. Version 2 uses (T − T_init)/ΔT.
2. Steady states replace the fixed end time of version 1.
3. One unit system and a physical pressure channel (see above). Version 1 stored the Boussinesq input in thermal-diffusion units and the compressible target in free-fall units, with the pressure min–max normalized to [0, 1].
4. Boundary data. Version 2 uses per-wall complexity dials (constant, or 1–2 Fourier modes per wall; adiabatic top/bottom walls) instead of a fixed number of modes on all four walls, and adds the 5,000-pair classical-cavity training set and the shifted test set.
5. Split sizes are 4,000 / 5,000 / 200 / 200 / 200 (version 1: 4,000 / 200 / 200 / 200 with a different generator).

Loading

import torch
X, Y = torch.load("train/X.pt"), torch.load("train/Y.pt")           # (4000, 4, 64, 64)

# normalization used in the paper: per-sample, per-channel min-max of the INPUT, applied to both
mn = X.amin(dim=(2, 3), keepdim=True)
rg = (X.amax(dim=(2, 3), keepdim=True) - mn).clamp_min(1e-12)
Xn, Yn = (X - mn) / rg, (Y - mn) / rg

The raw finite-element output of the same generator at four resolutions is in Paired_Boussinesq_Compressible_Dataset; the 3D tensors are in NeuralConvection_3D_TrainTest.

Source

Generated with the solver and data-generation pipeline at https://github.com/Nurshat317/NeuralConvection

License

Released under CC BY 4.0. You are free to share and adapt this data, including commercially, provided you give appropriate credit and indicate any changes. The requested form of credit is a citation to the paper below.

Citation

If you use this dataset in your research, please cite:

@article{menglik2026neural,
  title         = {A Neural Surrogate Approach for Simulating Natural Convection Problems},
  author        = {Menglik, Nurshat and Shao, Alex and Hyde, David},
  journal       = {arXiv preprint arXiv:2606.25259},
  year          = {2026},
  eprint        = {2606.25259},
  archivePrefix = {arXiv},
  primaryClass  = {physics.comp-ph},
  url           = {https://arxiv.org/abs/2606.25259}
}

• Paper: arXiv:2606.25259
• Code: github.com/Nurshat317/NeuralConvection