Geometry Meets Physics (GMP)

Data-Efficient Pre-Training for Unstructured Neural PDE Solvers

Accepted at NeurIPS 2026

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📌 Overview

GMP (Geometry Meets Physics) is a disk-data-free pre-training framework for neural surrogate models on unstructured 3D geometries, tailored to both steady-state and transient physical regimes.

Instead of relying on massive, pre-computed simulation data stored on disk (which often consume terabytes of storage and suffer from severe I/O bottlenecks), GMP generates pre-training data purely on-the-fly:

• Steady-state regime (Geometry-driven): Employs intrinsic shape descriptors (coordinates, curvatures, normals, and SGD) to learn rich representations of complex 3D domains without running expensive offline simulations.
• Transient regime (Physics-driven): Leverages GPU-accelerated solvers to generate synthetic PDE dynamics online, enabling scalable pre-training for time-dependent evolutions without storage overhead.

For full code, benchmark datasets, and evaluation scripts, visit the official GitHub Repository.

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📦 Pre-Trained Checkpoints

This repository hosts official pre-trained checkpoints for GMP-Net and baseline architectures:

Model / Baseline	Pre-Training Stage	Regime	Checkpoint Path in Repo	Size
GMP-Net	Geometry Pre-Training	Steady-state	gmpnet/epoch-200.pth	~346 MB
GMP-Net	Physics Pre-Training	Transient	gmpnet_physics/epoch-199-EMA.ckpt	~174 MB
AB-UPT	Geometry Pre-Training	Steady-state	abupt/epoch-200.pth	~148 MB
Transolver++	Geometry Pre-Training (Surface)	Steady-state	transolver_pp_surface/epoch-200.pth	~106 MB
Transolver++	Geometry Pre-Training (Volume)	Steady-state	transolver_pp_volume/epoch-200.pth	~106 MB

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🚀 How to Download the Weights

Option 1: Download All Checkpoints into outputs_pretraining/ (Recommended)

Using Python:

from huggingface_hub import snapshot_download

# Downloads all model weights directly into the folder expected by the GMP codebase
snapshot_download(
    repo_id="thuerey-group/GMP",
    local_dir="outputs_pretraining",
    allow_patterns=["*.pth", "*.ckpt"],
)

Or with the hf CLI:

hf download thuerey-group/GMP --local-dir outputs_pretraining --include "*.pth" --include "*.ckpt"

Once downloaded, the directory matches the expected hierarchy in the codebase:

outputs_pretraining/
├── gmpnet/
│   └── epoch-200.pth
├── gmpnet_physics/
│   └── epoch-199-EMA.ckpt
├── abupt/
│   └── epoch-200.pth
├── transolver_pp_surface/
│   └── epoch-200.pth
└── transolver_pp_volume/
    └── epoch-200.pth

Option 2: Download a Specific Checkpoint

from huggingface_hub import hf_hub_download

checkpoint_path = hf_hub_download(
    repo_id="thuerey-group/GMP",
    filename="gmpnet/epoch-200.pth",
    local_dir="outputs_pretraining",
)

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🔬 Supported Downstream Benchmarks

The pre-trained models can be directly fine-tuned across six downstream engineering benchmarks on unstructured surface and volumetric meshes:

• DrivAerML: Automotive aerodynamics (3D Surface & Volume).
• SHIFT-Wing: Aerospace aerodynamics (NASA CRM wings under varying Mach/AoA).
• SHIFT-Crash (Steady): Vehicle structural deformation and Von Mises stress.
• Kuramoto–Sivashinsky (KS): 2D chaotic spatiotemporal dynamics.
• Flow Around Ellipse: 2D unsteady fluid mechanics past an elliptical obstacle.
• SHIFT-Crash (Transient): Autoregressive collision and impact dynamics rollout across 12 timesteps.

Refer to the GitHub Repository for Hydra fine-tuning commands.

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📜 Citation

If you use these pre-trained weights or the GMP framework in your research, please cite our paper:

@inproceedings{medrano2026geometry,
  title={Geometry Meets Physics: Data-Efficient Pre-Training for Unstructured Neural PDE Solvers},
  author={Medrano-Navarro, Luis and Baldan, Giacomo and Liu, Qiang and Holzschuh, Benjamin and Hagnberger, Jan and Niepert, Mathias and Thuerey, Nils},
  booktitle={The Fortieth Annual Conference on Neural Information Processing Systems},
  year={2026},
  url={https://openreview.net/forum?id=jidnQA2TIz}
}

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📄 License

The checkpoints and code are released under the Apache 2.0 License.