delta-lab-ai/fundamental-physics-neural-operators

Fundamental Physics Neural Operators

Paper: Learning Data-Efficient and Generalizable Neural Operators via Fundamental Physics Knowledge Published at: ICLR 2026 Authors: Siying Ma, Mehrdad M. Zadeh, Mauricio Soroco, Wuyang Chen, Jiguo Cao, Vijay Ganesh Affiliations: Simon Fraser University, Georgia Institute of Technology Project Page: https://sites.google.com/view/sciml-fundemental-pde

Overview

We propose a multiphysics training framework that jointly learns from both original PDEs and their simplified basic forms (decomposed fundamental physics terms). This approach improves data efficiency, long-term physical consistency, and out-of-distribution generalization across 1D/2D/3D PDE problems. The method is architecture-agnostic and demonstrates consistent improvements in nRMSE.

Checkpoints

All checkpoints are Transformer-based neural operators (VideoMAE architecture, see Appendix B of the paper).

Naming Convention

{Model}_{PDE}_{dsN_P_B}.pt

• Model prefix:
  • Transformer = Baseline (trained only on original PDE)
  • TransformerAux = Ours (jointly trained on original PDE + decomposed basic form)
• PDE suffix:
  • 3D = 3D Incompressible Navier-Stokes
  • _RD = 2D Diffusion-Reaction
  • (no suffix) = 2D Incompressible Navier-Stokes
• Data composition dsN_P_B: N = equivalent baseline samples, P = PDE samples, B = basic form samples

Available Checkpoints

File	PDE	Type	Size	Reproduces
navier_stokes_3d/Transformer3D_ds64_32_96.pt	3D Navier-Stokes	Baseline	3.32 GB	Table 6, Figure 10
navier_stokes_3d/TransformerAux3D_ds64_32_96.pt	3D Navier-Stokes	Ours	3.32 GB	Table 6, Figure 10
diffusion_reaction_2d/Transformer_RD_ds128_64_192.pt	2D Diffusion-Reaction	Baseline	2.54 GB	Table 5, Figure 9
diffusion_reaction_2d/TransformerAux_RD_ds128_64_192.pt	2D Diffusion-Reaction	Ours	2.54 GB	Table 5, Figure 9
navier_stokes_2d/TransformerAux_ds16_8_48.pt	2D Navier-Stokes	Ours	1.25 GB	Figure 9, Figure 11

Usage

import torch

# Download checkpoint
from huggingface_hub import hf_hub_download

ckpt_path = hf_hub_download(
    repo_id="delta-lab-ai/fundamental-physics-neural-operators",
    filename="navier_stokes_3d/TransformerAux3D_ds64_32_96.pt"
)

# Load
checkpoint = torch.load(ckpt_path, map_location="cpu")

Citation

@inproceedings{ma2026learning,
  title={Learning Data-Efficient and Generalizable Neural Operators via Fundamental Physics Knowledge},
  author={Ma, Siying and Zadeh, Mehrdad M. and Soroco, Mauricio and Chen, Wuyang and Cao, Jiguo and Ganesh, Vijay},
  booktitle={International Conference on Learning Representations (ICLR)},
  year={2026}
}

License

MIT