ZienkiFlowNet

Graph neural network predicting incompressible 2D Stokes/Navier–Stokes solutions (vx, vy, p) and the inlet flow rate Q from geometry only, trained on CFD reference solutions produced by the Zienki finite-element solver.

Layout

ZienkiFlowNet/
├── GCNN/                 ← Python package
│   ├── dataset.py
│   ├── model.py
│   ├── train.py
│   ├── infer.py
│   ├── evaluate.py
│   ├── utils.py
│   └── README.md
└── README.md

../cfd_database/          ← reference dataset (sibling, not tracked here)
└── cases/
    └── case_XXXX/
        ├── params.json
        ├── result.vtu
        └── result.post.json

The dataset directory is expected as a sibling of ZienkiFlowNet/. It can be overridden with --cases on the CLI.

Quickstart

PYBIN=/path/to/venv/bin/python
$PYBIN -m GCNN.dataset --build                # build cached PyG dataset
$PYBIN -m GCNN.train   --epochs 300           # train
$PYBIN -m GCNN.evaluate                       # evaluate on validation split
$PYBIN -m GCNN.infer   --case ../cfd_database/cases/case_0000

Architecture (current best, v5)

• Encoder: per-node features (8 geom + 4 obs + 2 wall normal) + 16-dim Laplacian-eigenvector positional encoding (MLP_pos, MLP_spec heads).
• Processor: 8 × MeshGraphNet blocks + 8 × CellBlock (FE-native TRI3 message-passing using P1 basis gradients), interleaved with global-token cross-attention and per-graph multi-head boundary cross-attention every two layers.
• Decoder: per-node (vx_n, vy_n, p_n) + global head for Q.
• Hard BC projection in scaled space: walls u=0, inlet p=1, outlet p=0.

Training regime

JEPA-style auto-supervision: a fraction of nodes carry the ground-truth field as input (context), the rest are masked (targets). The mask ratio anneals on a cosine schedule from 0.30 → 1.00 over the training run, so the final epochs match the inference setting (pure geometry).

Losses: node MSE on targets + BC residual + global Q + scaled divergence on cells.