disco-ns

Trajectories used in the ICML 2026 paper Test-time Generalization for Physics through Neural Operator Splitting (Serrano, Han, Oyallon, Ho, Morel).

2D simulations of three closely-related physics regimes on a periodic square domain $[0, 2\pi]^2$, resolved at 256×256 (downsampled from a 512×512 spectral solver):

• euler — inviscid 2D vorticity transport ($\nu = 0$).
• navier_stokes — incompressible Navier–Stokes in vorticity form. Diffusion viscosities are sampled at 16 log-spaced values in $[10^{-4}, 10^{-2}]$.
• diffusion — pure diffusion (no advection), same 16 viscosities.

Composing the Euler and diffusion operators recovers the Navier–Stokes dynamics — this dataset is what the paper uses to demonstrate test-time operator splitting on the 2D Navier–Stokes benchmark.

Files

File	Split	Size	Trajectories per equation
ns_train_gpu0.h5 … ns_train_gpu7.h5	train	8 × 38 GB	1024 each (8192 total per equation across shards)
ns_val_512.h5	validation	6.7 GB	512
ns_test_gpu0.h5	test	40 GB	held-out trajectories

Per-shard counts and the viscosity grid are exposed as root-level HDF5 attributes (see below).

HDF5 layout

Each file contains three sibling datasets — one per equation type:

/euler          shape (N, 50, 256, 256)  float32   — vorticity ω(t, x, y)
/navier_stokes  shape (N, 50, 256, 256)  float32   — vorticity ω(t, x, y)
/diffusion      shape (N, 50, 256, 256)  float32   — vorticity ω(t, x, y)

with N = 1024 per training shard. T = 4.0 (horizon), n_snapshots = 50.

Root-level .attrs:

Attribute	Value	Meaning
T	4.0	total integration time
n_snapshots	50	number of saved frames per trajectory
sim_res	512	simulation resolution
save_res	256	downsampled saved resolution
viscosities	[1e-4 … 1e-2] (16 values, log-spaced)	viscosities for the NS / diffusion runs (Euler has ν=0)
num_gpus	8	total shards
gpu_id	0…7	this shard's index
euler_count, ns_count, diff_count	1024	per-equation trajectory counts
euler_start, ns_start, diff_start	0	offset within the global trajectory index (for resharding)

Reproducing the paper's Navier–Stokes results

The training pipeline expects all 8 train shards and the val file:

from huggingface_hub import hf_hub_download
import os

REPO = "sogeeking/disco-ns"
LOCAL = "./datasets/euler_ns_short"
os.makedirs(LOCAL, exist_ok=True)

# Train shards (≈300 GB total — caches under ~/.cache/huggingface)
for i in range(8):
    src = hf_hub_download(REPO, f"ns_train_gpu{i}.h5", repo_type="dataset")
    dst = os.path.join(LOCAL, f"trajectories_gpu{i}.h5")
    if not os.path.exists(dst):
        os.symlink(src, dst)

# Validation
src = hf_hub_download(REPO, "ns_val_512.h5", repo_type="dataset")
os.symlink(src, os.path.join(LOCAL, "ns_val_512.h5"))

The downloaded files are then read by train/train_euler_diffusion_aggregate.py and the matching SLURM launcher under bash/euler/.

Quick load

import h5py
from huggingface_hub import hf_hub_download

local = hf_hub_download("sogeeking/disco-ns", "ns_train_gpu0.h5", repo_type="dataset")
with h5py.File(local, "r") as f:
    ns = f["navier_stokes"]   # shape (1024, 50, 256, 256)
    print("viscosities:", f.attrs["viscosities"])
    sample = ns[0]            # one trajectory: (50, 256, 256)

Code: https://github.com/LouisSerrano/neural-operator-splitting