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Finite Volume Features, Global Geometry Representations, and Residual Training for Deep Learning-based CFD Simulation
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Proposes Shortest Vector and Directional Integrated Distance global geometry features, Finite Volume Features as node/edge attributes in graph convolutions, and residual training with low-resolution data to reduce flow-field prediction error of GNN CFD surrogates by up to 41%.
Problem
GNN-based CFD surrogates receive very limited geometric information about immersed objects and ignore finite volume cell characteristics (cell volume, face area normal, face centroid), so they must propagate boundary information locally through message passing.
Approach
Add mesh-derived global geometry features (SV, DID) to input nodes, embed finite volume cell/face attributes into graph convolutions as node and edge attributes (FVGC), and train on residuals relative to upsampled low-resolution flow fields.
Key results
- CFDGCN with residual training, FVF and Geo reduces MSE from 0.1211e-2 to 0.0719e-2 (about 41%) on AirfRANS with vanilla graph convolution.
- MeshGraphNet with Geo and FVF reduces MSE from 5.7571e-2 to 3.3811e-2 (about 41%) on AirfRANS.
- Chen-GCNN with SAGE convolution reduces MAE by about 82% (6.7103e-2 to 1.1982e-2) on 2DSHAPES.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Add geometric features (SV and DID) (ablation) | MeshGraphNet · AirfRANS | MSE: 5.7571 -> 3.4683 | Helped |
| Add FVF to geometric features (ablation) | MeshGraphNet · AirfRANS | MSE: 3.4683 -> 3.3811 | Helped |
| Add geometric features (SV and DID) (ablation) | BSMS-GNN · AirfRANS | RMSE: 7.7589 -> 6.7498 | Helped |
| Add FVF to geometric features (ablation) | BSMS-GNN · AirfRANS | RMSE: 6.7498 -> 6.1919 | Helped |
| Add geometric features (SV and DID) (ablation) | Chen-GCNN with Invariant Edge Convolution · 2DSHAPES | MAE: 1.1590 -> 0.9727 | Helped |
| Add FVF to geometric features (ablation) | Chen-GCNN with Invariant Edge Convolution · 2DSHAPES | MAE: 0.9727 -> 0.8491 | Helped |
| Add geometric features (SV and DID) (ablation) | Chen-GCNN with SAGE Convolution · 2DSHAPES | MAE: 6.7103 -> 3.8041 | Helped |
| Add FVF to geometric features (ablation) | Chen-GCNN with SAGE Convolution · 2DSHAPES | MAE: 3.8041 -> 1.1982 | Helped |
| Add geometric features (SV and DID) (ablation) | Graph U-Net with SAGE Convolution · AirfRANS | test loss: 1.816 -> 1.786 | Helped |
| Add FVF to geometric features (ablation) | Graph U-Net with SAGE Convolution · AirfRANS | test loss: 1.786 -> 1.441 | Helped |
| Add geometric features (SV and DID) (ablation) | Graph U-Net with Vanilla Graph Convolution · AirfRANS | test loss: 15.310 -> 12.709 | Helped |
| Add FVF to geometric features (ablation) | Graph U-Net with Vanilla Graph Convolution · AirfRANS | test loss: 12.709 -> 4.544 | Helped |
Surprising findings
- Adding geometric and FVF features to Chen-GCNN with SAGE convolution gives about 82% MAE reduction, larger than the invariant edge convolution gain of about 27%.
- Residual training gave almost no extra gain over FVF+Geo for CFDGCN with SAGE convolution (0.0631 vs 0.0628 x10^-2).
Limitations
- DID computation is relatively slow because angle segments are computed sequentially.
- Residual training was only evaluated on CFDGCN with AirfRANS, since only CFDGCN takes low-resolution input.
- Some model variants changed widths or sizes, so gains may partly reflect capacity differences (e.g., Graph U-Net with FVF has 160k vs 66k parameters for SAGE).
Experimental setup
Datasets: AirfRANS 2DSHAPES coarse-AirfRANS
Benchmarks: AirfRANS 2DSHAPES
Metrics: MSE MAE RMSE test loss volume MSE surface MSE
Baselines: MeshGraphNet BSMS-GNN Chen-GCNN Graph U-Net CFDGCN
Builds on: MeshGraphNet BSMS-GNN Graph U-Net GraphSAGE signed distance function
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