Graph Convolutional Neural Networks for Body Force Prediction
This work addresses the challenge of applying data-driven models to spatially unstructured data for engineers and scientists, offering a method that is invariant to measurement order and resolution.
This paper tackles the problem of predicting global properties from spatially irregular measurements, which are common in scientific and engineering processes. The authors developed a Graph Convolutional Neural Network (GCNN) that predicts the drag force associated with laminar flow around airfoils from scattered velocity measurements with a validation R^2 above 0.98 and a Normalized Mean Squared Error below 0.01.
Many scientific and engineering processes produce spatially unstructured data. However, most data-driven models require a feature matrix that enforces both a set number and order of features for each sample. They thus cannot be easily constructed for an unstructured dataset. Therefore, a graph based data-driven model to perform inference on fields defined on an unstructured mesh, using a Graph Convolutional Neural Network (GCNN) is presented. The ability of the method to predict global properties from spatially irregular measurements with high accuracy is demonstrated by predicting the drag force associated with laminar flow around airfoils from scattered velocity measurements. The network can infer from field samples at different resolutions, and is invariant to the order in which the measurements within each sample are presented. The GCNN method, using inductive convolutional layers and adaptive pooling, is able to predict this quantity with a validation $R^{2}$ above 0.98, and a Normalized Mean Squared Error below 0.01, without relying on spatial structure.