This dataset contains 4D scalar phi4 lattice configurations generated with a Wolff + Fourier-Accelerated HMC sampler, together with the 4D score-model code, retained checkpoints, generated samples and analysis results.

Both JLD2 and NumPy variants are retained: JLD2 provides native Julia access, while NPZ is the published Python/Hugging Face format. For each lattice size, the two variants contain the same configurations and corresponding metadata values; the container formats and metadata key names differ.

Files

File	Format	Lattice	Shape of `cfgs`	dtype
`trainingdata/cfgs_wolff_fahmc_k=0.145_l=0.9_8^4.jld2`	JLD2	`8^4`	`(8, 8, 8, 8, 5120)`	`Float64`
`trainingdata/cfgs_wolff_fahmc_k=0.145_l=0.9_8^4.npz`	NPZ	`8^4`	`(8, 8, 8, 8, 5120)`	`float64`
`trainingdata/cfgs_wolff_fahmc_k=0.145_l=0.9_16^4.jld2`	JLD2	`16^4`	`(16, 16, 16, 16, 5120)`	`Float64`
`trainingdata/cfgs_wolff_fahmc_k=0.145_l=0.9_16^4.npz`	NPZ	`16^4`	`(16, 16, 16, 16, 5120)`	`float64`

Repository layout

WolffFAHMC_ND.jl: shared dimension-independent sampler engine.
WolffFAHMC_4D.jl: 4D wrappers and analysis functions. Importing it no longer starts a production run.
trainingdata/: HMC training configurations in NPZ and JLD2 formats.
train_phi4_4d.py, sample_phi4_4d.py: score-model training and reverse-SDE sampling entry points.
diffusion_lightning.py, phi4_action.py: bundled diffusion and lattice action utilities; no DM parent-directory import is required.
networks_nd.py: bundled 2D/3D reference implementation used by the 4D embedding test.
julia/CorrelationUtils.jl: bundled dimension-generic propagator utilities.
requirements.txt, Project.toml, Manifest.toml: Python requirements and a version-locked Julia environment.
runs/: retained checkpoints, generated samples, metrics and propagators.
scripts/run_production_4d.jl: explicit production example. Generated JLD2 files are kept beside their NPZ counterparts in trainingdata/.
results/production/: complete production diagnostics (CSV and plots).
results/scan_kappa_wolff_fahmc/: kappa-scan tables and plots.

Instantiate the declared Julia dependencies and run the production example from this repository root with:

julia --project=. -e 'using Pkg; Pkg.instantiate()'
julia --project=. scripts/run_production_4d.jl

Each .npz file contains:

cfgs: field configurations, with samples on the last axis.
kappa: hopping parameter.
lambda: quartic coupling.
N: lattice size.
n_samples: number of stored configurations.
epsilon_final: final HMC step size.
acc_rate: production HMC acceptance rate.

In Python, one configuration is cfgs[:, :, :, :, i], where i is the zero-based sample index.

Download

Install the Hugging Face Hub client:

pip install -U huggingface_hub

Download the full self-contained snapshot:

hf download YangyangTan/4Dphi4 \
  --repo-type dataset \
  --local-dir 4Dphi4

Download one file:

hf download YangyangTan/4Dphi4 \
  "trainingdata/cfgs_wolff_fahmc_k=0.145_l=0.9_8^4.npz" \
  --repo-type dataset \
  --local-dir .

Load with NumPy

import numpy as np

path = "trainingdata/cfgs_wolff_fahmc_k=0.145_l=0.9_8^4.npz"
data = np.load(path)

cfgs = data["cfgs"]
kappa = data["kappa"].item()
lam = data["lambda"].item()
N = data["N"].item()

phi0 = cfgs[:, :, :, :, 0]
print(cfgs.shape, cfgs.dtype)
print(kappa, lam, N)

You can also download directly from Python:

from huggingface_hub import hf_hub_download
import numpy as np

path = hf_hub_download(
    repo_id="YangyangTan/4Dphi4",
    filename="trainingdata/cfgs_wolff_fahmc_k=0.145_l=0.9_8^4.npz",
    repo_type="dataset",
)

data = np.load(path)
cfgs = data["cfgs"]

Train the score model

Run the scripts from the repository root on an NVIDIA GPU. The repository is self-contained and does not import source files from a parent DM directory.

The Python dependencies are PyTorch, PyTorch Lightning, torch-ema, NumPy, PyYAML, tqdm and Matplotlib. Install them with:

python -m pip install -r requirements.txt

The current implementation uses CUDA and torch.compile. SciPy is included in the requirements only for the optional RK45 probability-flow ODE sampler.

The NPZ layout must be (L, L, L, L, n_samples). The loader moves only the final sample axis to the batch position and inserts the scalar-field channel, producing network input (n_samples, 1, L, L, L, L).

The retained production configuration is:

# L=8
python train_phi4_4d.py \
  --data_path trainingdata/cfgs_wolff_fahmc_k=0.145_l=0.9_8^4.npz \
  --sigma 305 --channels 36,64,128,256 \
  --normalization minmax --final_bias --zero_mode_loss_weight 0 \
  --lr 1e-3 --batch_size 64 --epochs 20000 \
  --ema_start 0 --num_ckpts 100 --device cuda:0

# L=16
python train_phi4_4d.py \
  --data_path trainingdata/cfgs_wolff_fahmc_k=0.145_l=0.9_16^4.npz \
  --sigma 1249 --channels 36,64,128,256 \
  --normalization minmax --final_bias --zero_mode_loss_weight 0 \
  --lr 1e-3 --batch_size 64 --epochs 20000 \
  --ema_start 0 --num_ckpts 100 --device cuda:0

Omit --sigma to estimate it from the maximum pairwise distance in the normalized training set. Checkpoints are saved on a logarithmic epoch schedule under runs/<run-name>/models/; the exact configuration and CSV metrics are stored in training_config.yaml and logs/version_*/metrics.csv.

Resume training

Use the same data, sigma, channels, normalization, bias, zero-mode weight and output suffix as the original run. --epochs is the final total epoch, not the number of additional epochs.

RUN=runs/phi4_4d_L8_k0.145_l0.9_ncsnpp_sigma305_ch36-64-128-256_minmax_bias_directscore_k0w0
python train_phi4_4d.py \
  --data_path trainingdata/cfgs_wolff_fahmc_k=0.145_l=0.9_8^4.npz \
  --sigma 305 --channels 36,64,128,256 \
  --normalization minmax --final_bias --zero_mode_loss_weight 0 \
  --lr 1e-3 --batch_size 64 --epochs 20000 \
  --ema_start 0 --num_ckpts 100 --device cuda:0 \
  --resume_from_checkpoint "$RUN/models/epoch=6021.ckpt"

Generate samples

Keep a checkpoint in its original run directory beside training_config.yaml; the sampler reads that file to reconstruct the channel widths and final-convolution bias. Sampling uses EMA weights by default.

RUN=runs/phi4_4d_L8_k0.145_l0.9_ncsnpp_sigma305_ch36-64-128-256_minmax_bias_directscore_k0w0
python sample_phi4_4d.py \
  --checkpoint "$RUN/models/epoch=4929.ckpt" \
  --num_samples 256 --num_steps 2000 --schedule linear --seed 0

The default output is $RUN/data/samples_em_steps2000_linear_ep4929_seed0.npy, with shape (L, L, L, L, n_samples). Use --no_ema for raw network weights, --symmetrize_z2 for the Z2-symmetrized-score diagnostic, or --output_dir DIR to choose another output directory.

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