llingsch/phaedra-tokens

Phaedra token datasets

Tokenized versions of three compressible-Euler datasets from the Poseidon / PDEgym collection, produced with the four tokenizers of Phaedra: Learning High-Fidelity Discrete Tokenization for the Physical Sciences (NeurIPS 2026): Phaedra, FSQ, VQ-VAE-2 and a continuous autoencoder. They are the inputs of the neural operators and masked autoencoders in the paper. Models: llingsch/phaedra · code: https://github.com/camlab-ethz/Phaedra · project page: https://camlab-ethz.github.io/Phaedra/.

key	source (Hugging Face)	description
KH	camlab-ethz/CE-KH	shear (Kelvin–Helmholtz) initial conditions
RC	camlab-ethz/CE-CRP	curved Riemann problems
RKH	camlab-ethz/CE-RPUI	4-quadrant Riemann problems with uncertain interfaces

Each source dataset has 10,000 trajectories × 21 time steps on a 128×128 grid of the unit square ($t \in [0, 1]$). Trajectory $i$ here is trajectory $i$ of the source dataset assembled in numeric chunk order (data_0.nc, data_1.nc, …, data_13.nc; scripts/prepare_poseidon_data.py in the code does this and verifies the result). Splits: trajectories 0–9639 train, 9640–9759 validation, 9760–9999 test (also stored as the split_*_range attributes).

Files

file	tokenizer	dtype	shape	size
tokens/phaedra/CEU2D_KelvinHelmholtzTokens.nc	phaedra	uint16	(10000, 21, 32, 32)	3.44 GB
tokens/phaedra/CEU2D_RiemannCurvedTokens.nc	phaedra	uint16	(10000, 21, 32, 32)	3.44 GB
tokens/phaedra/CEU2D_RiemannKelvinHelmholtzTokens.nc	phaedra	uint16	(10000, 21, 32, 32)	3.44 GB
tokens/fsq/CEU2D_KelvinHelmholtzTokens.nc	fsq	int32	(10000, 21, 32, 32)	3.44 GB
tokens/fsq/CEU2D_RiemannCurvedTokens.nc	fsq	uint16	(10000, 21, 32, 32)	1.72 GB
tokens/fsq/CEU2D_RiemannKelvinHelmholtzTokens.nc	fsq	uint16	(10000, 21, 32, 32)	1.72 GB
tokens/vqvae2/CEU2D_KelvinHelmholtzTokens.nc	vqvae2	int32	(10000, 21, 32, 32)	2.79 GB
tokens/vqvae2/CEU2D_RiemannCurvedTokens.nc	vqvae2	int32	(10000, 21, 32, 32)	2.95 GB
tokens/vqvae2/CEU2D_RiemannKelvinHelmholtzTokens.nc	vqvae2	int32	(10000, 21, 32, 32)	2.86 GB
latents/continuous/CEU2D_KelvinHelmholtzLatents.nc	continuous	float32	(10000, 8, 4, 8, 32, 32)	5.65 GB
latents/continuous/CEU2D_RiemannCurvedLatents.nc	continuous	float32	(10000, 8, 4, 8, 32, 32)	6.32 GB
latents/continuous/CEU2D_RiemannKelvinHelmholtzLatents.nc	continuous	float32	(10000, 8, 4, 8, 32, 32)	5.77 GB

All files are netCDF-4 (netCDF4, xarray).

• tokens/phaedra: <var>_amp (amplitude, 0–1023) and <var>_morph (morphology) for rho, u, v, p, dims (member, time=21, token_x=32, token_y=32). Morphology ids are stored shifted by the morphology_offset attribute (1024); subtract it before decoding (range 0–8639).
• tokens/fsq: <var>_tokens (0–8639), same dims (int32 for KH, uint16 for RC/RKH — values identical).
• tokens/vqvae2: <var>_amp = VQ-VAE-2 top codes (0–4095, native 16×16 grid replicated 2×2 onto 32×32; recover with amp[..., ::2, ::2]) and <var>_morph = bottom codes (0–16383, 32×32).
• latents/continuous: latents float32 (member, time=8, var=4, ch=8, 32, 32); the time axis holds only the even source steps $t = 0, 2, …, 14$ (attribute time_indices).

import netCDF4 as nc
ds = nc.Dataset("tokens/phaedra/CEU2D_KelvinHelmholtzTokens.nc")
amp = ds["rho_amp"][9760, 14]                                   # test trajectory 0, t = 14
morph = ds["rho_morph"][9760, 14] - ds.getncattr("morphology_offset")
# decode: from tokenizer.pretrained import load_tokenizer; load_tokenizer("Phaedra_AE_FSQ_4x4").decode(...)

Decoded fields are normalized; physical values are $x = x' \sigma + \mu$ (μ / σ):

data	ρ	u	v	p
KH (CE-KH)	0.75 / 0.22776	-0.016416 / 0.112602	5e-05 / 0.044217	1 / 0.0083488
RC (CE-CRP)	0.548238 / 0.322666	0.00042 / 0.275455	0.0026327 / 0.275455	0.552022 / 0.169886
RKH (CE-RPUI)	0.543686 / 0.361854	-0.00332036 / 0.210691	0.00215155 / 0.215305	0.548822 / 0.199823

Integrity

SHA256SUMS lists every file. Every token id of every file was range-checked against its codebook (no fill values), the VQ-VAE-2 2×2 replication was checked everywhere, and all latents are finite.

License and attribution

CC-BY-NC-4.0, inherited from the source datasets (Poseidon / PDEgym, CC BY-NC 4.0). If you use these files, please cite the paper below and Poseidon (Herde et al., Poseidon: Efficient Foundation Models for PDEs, NeurIPS 2024).

@inproceedings{lingsch2026phaedra,
  title         = {Phaedra: Learning High-Fidelity Discrete Tokenization for the Physical Sciences},
  author        = {Lingsch, Levi and Kissas, Georgios and Jakubik, Johannes and Mishra, Siddhartha},
  booktitle     = {Advances in Neural Information Processing Systems},
  year          = {2026},
  eprint        = {2602.03915},
  archivePrefix = {arXiv},
  url           = {https://arxiv.org/abs/2602.03915}
}