Flow reconstruction in time-varying geometries using graph neural networks

TL;DR

A comparative analysis shows that the GACN consistently outperforms both a conventional Convolutional Neural Network (CNN) and cubic interpolation methods on the DNS and PIV test sets by achieving lower reconstruction errors and better capturing fine-scale turbulent structures.

Abstract

The paper presents a Graph Attention Convolutional Network (GACN) for flow reconstruction from very sparse data in time-varying geometries. The model incorporates a feature propagation algorithm as a preprocessing step to handle extremely sparse inputs, leveraging information from neighboring nodes to initialize missing features. In addition, a binary indicator is introduced as a validity mask to distinguish between the original and propagated data points, enabling more effective learning from sparse inputs. Trained on a unique data set of Direct Numerical Simulations (DNS) of a motored engine at a technically relevant operating condition, the GACN shows robust performance across different resolutions and domain sizes and can effectively handle unstructured data and variable input sizes. The model is tested on previously unseen DNS data as well as on an experimental data set from Particle Image Velocimetry (PIV) measurements that were not considered during training. A comparative analysis shows that the GACN consistently outperforms both a conventional Convolutional Neural Network (CNN) and cubic interpolation methods on the DNS and PIV test sets by achieving lower reconstruction errors and better capturing fine-scale turbulent structures. In particular, the GACN effectively reconstructs flow fields from domains up to 14 times larger than those observed during training, with the performance advantage increasing for larger domains.

Figures (10)

• Figure 1: Engine geometry and illustration of data generation showing the velocity magnitude distribution on three $xz$ slices.
• Figure 2: Schematic of the GACN model architecture and its internal structure.
• Figure 3: The architecture of the CNN model used for comparison.
• Figure 4: Results for one panel at -60 CAD from the DNS panel test set. Rows from top to bottom show: GACN, CNN, and interpolation results. Columns from left to right present: input with 1% retained information, model prediction, DNS ground truth, and absolute error between prediction and ground truth.
• Figure 5: Results for one slice at -90 CAD from the DNS slice test set. Rows from top to bottom show: GACN, CNN, and interpolation results. Columns from left to right present: input with 1% retained information, model prediction, DNS ground truth, and absolute error between prediction and ground truth. The dark grey outline highlights the engine geometry. The purple square in the DNS column illustrates the size of a training panel and is not a velocity feature.