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Phaedra: Learning High-Fidelity Discrete Tokenization for the Physical Sciences

NeurIPS 2026 · Image generation › Autoregressive and latent generation · approach: Generative latent space tooling

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Phaedra is a discrete tokenizer for 2D PDE fields that splits latents into a vector-quantized morphology stream and a finely scalar-quantized amplitude stream, outperforming image tokenizers (FSQ, VQ-VAE-2, IBQ, VAR, Cosmos) on reconstruction and showing zero-shot transfer plus proof-of-concept downstream results.

Problem

Image tokenizers designed for natural images perform poorly on physical fields with heavy-tailed dynamic range and requiring exact physical magnitudes and spectral fidelity, limiting the use of discrete tokens in physics foundation models.

Approach

Factorize the latent by channel into a morphology stream (multi-dimensional FSQ with 8640 codes) and a 1-D amplitude stream (FSQ with 1024 levels), inspired by shape-gain quantization, then recombine with a learned channel-mixing convolution.

Key results

• Phaedra reduces ID nMAE to 1.522 versus 2.603 for FSQ and 3.229 for VAR_large (over 40% reduction vs strongest baselines).
• Phaedra compresses a 65.0 GB training dataset to 3.44 GB (94.7% savings) at ID nMAE 1.522.
• On operator learning, Phaedra achieves 27.21% relative L1 on RC versus 119.0% for the continuous transformer and 38.05% for FSQ.

Surprising findings

• A continuous autoencoder achieves the best in-distribution reconstruction, yet discrete tokenizers degrade less out of distribution (continuous AE error rises ~70% on OD1 while Phaedra improves).
• Continuous transformer fails to converge on the RC downstream dataset (119% relative L1).

Limitations

• Tokenizes each field component independently, ignoring inter-variable coupling.
• Evaluated only on 2D PDEs on uniform grids; 3D and irregular meshes left as future work.
• Convolutional decoder yields soft rather than exact amplitude-morphology disentanglement.

Experimental setup

Datasets: Poseidon pretraining suite PDEGym compressible Euler PDEGym incompressible Navier-Stokes Sentinel-2 L1C ERA5 ImageNet (grayscale)

Benchmarks: Poseidon compressible Euler/Navier-Stokes ID/OOD splits Sentinel-2 L1C ERA5 ImageNet grayscale operator learning KH/RC/RKH masked autoencoding (75%)

Metrics: nMAE nRMSE minimal spectral coherence local variance error relative L1 rL2 compression ratio

Baselines: FSQ VQ-VAE-2 IBQ VAR Cosmos DI Continuous AE FNO CNO ViT

Builds on: FSQ VQ-VAE-2 VAR IBQ RQ-VAE

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