---
license: apache-2.0
library_name: transformers
tags:
- meshgraphnet
- graph-neural-network
- cfd
- cylinder-flow
- custom_code
---

# MeshGraphNet — cylinder_flow

[MeshGraphNet](https://arxiv.org/abs/2010.03409) (DeepMind, ICLR 2021) for flow around a cylinder.
Given the velocity at every mesh node, it predicts the velocity change for the next time step.

## Usage

```python
from transformers import AutoModel

model = AutoModel.from_pretrained("ketiswp/meshgraphnet-hf", trust_remote_code=True)

inputs = model.prepare_inputs(cells, mesh_pos, node_type, velocity)  # one cylinder_flow time step
delta = model(**inputs).delta_velocity                              # [N, 2]
trajectory = model.rollout(**inputs, num_steps=599)                 # [600, N, 2]
```

## Training

Trained on DeepMind `cylinder_flow` with the original settings: one frame per step (frames 1..598,
shuffle buffer 10000), velocity noise std 0.02, Adam with lr `1e-4 * 0.1^(step/5e6) + 1e-6`, 10M steps,
first 1000 steps only collect normalizer statistics, Sonnet weight init, float32.

`split_first_linear` holds the first Linear of each layer per input
(`W [h_s; h_r; e] = W_s h_s + W_r h_r + W_e e`), so sender/receiver projections are computed once per
node instead of building the per-edge concatenation. Same weights and outputs as without it.

## Results

CylinderFlow, in the format of Table 1 of the paper.

| | # nodes (avg.) | # steps | t_model ms/step | t_full ms/step | t_GT ms/step | RMSE 1-step ×10⁻³ | RMSE rollout-50 ×10⁻³ | RMSE rollout-all ×10⁻³ | GPU |
|---|---|---|---|---|---|---|---|---|---|
| paper | 1885 | 600 | 21 | 23 | 820 | 2.34 ± 0.12 | 6.3 ± 0.7 | 40.88 ± 7.2 | NVIDIA Tesla V100 |
| this model | 1885 | 600 | 4.0 | 4.4 | – | 2.35 ± 0.09 | 6.67 ± 0.30 | 55.83 ± 3.97 | NVIDIA RTX 6000 Ada Generation |

This model: 100 test trajectories; ± is the standard error over trajectories. Timings on one GPU,
batch 1, float32; `t_full` includes rebuilding the graph from the mesh every step.

## License

Apache-2.0, as the original [DeepMind](https://github.com/google-deepmind/deepmind-research/tree/master/meshgraphnets)
and [medav/meshgraphnets-torch](https://github.com/medav/meshgraphnets-torch) code.