Networks for fields
How a network can see a whole geometry and field at once: convolutions on grids, message passing on meshes, and neural operators that map functions to functions.
Start the unit Grids, meshes and operators
- 5.1Grids, meshes and point cloudsThe same shape as a grid, a graph or a point cloud: how geometry and fields become tensors.
- 5.2Convolutions and U-NetsA learned stencil slid over a grid, at several scales, with shortcuts for fine detail.
- 5.3Graph networks and MeshGraphNetsEvery mesh node updates from its neighbours, layer after layer.
- 5.4Time stepping and rolloutsPredict the next state from the current one, then feed predictions back in; errors grow with every step.
- 5.5Neural operatorsDeepONet, FNO and GINO learn maps between functions, so the model is not tied to one grid.
You can thenChoose and train a grid, graph or operator model.
Read and build
ReadU-Net: Convolutional Networks for Biomedical Image SegmentationRonneberger, Fischer, Brox · MICCAI 2015 ↗Deep Learning Methods for Reynolds-Averaged Navier–Stokes Simulations of Airfoil FlowsThuerey et al. · AIAA Journal 2020 ↗MeshGraphNetsOn this site · ICLR 2021FNOOn this site · ICLR 2021DeepONetOn this site · Nature Machine Intelligence 2021
BuildTrain a U-Net on gridded AirfRANS, a MeshGraphNet on cylinder flow and an FNO on Darcy flow.
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