Using Graph Neural Networks for unstructured grid problems

Say you have some kind of internal flow problem where you need to classify the flow into two classes. If the geometry is complex it may be difficult to do this efficiently with a convolutional neural network, since these networks usually use data on a regularly spaced grid.

One alternative is to use a graph neural network (GNN) where nodes are connected by edges. Below is an example, where the colors show two classes. It is from a river network with ice and water. We found a GNN was much more efficient and more accurate than a CNN for this problem.

This type of data structure can be used for problems with complex geometries and deformation

credit: Yifan Qu

Using Graph Neural Networks (GNNs) for Emulation

Many engineering problems involve spatial-temporal dynamics. We often forecast these by solving large sets of coupled partial differential equations, which is expensive. For applications needing a prediction quickly, this is often not feasible. Recent methods, such as neural operators or sequence-to-sequence learning, offer different ways to approach this. We are exploring using graph neural networks, and sequence-to-sequence learning, with an LSTM in both the encoder and decoder, enabling the predicted sequence to have a different length than the input sequence for these types of problems

Please contact me if you are interested!