Leveraging Steerable Equivariant Graph Neural Networks for Data-Driven Flow Modeling
Nikita Kozak, Stanford University
In practical applications of computational fluid dynamics (CFD), turbulence is often represented using simplifying assumptions to make the simulations computationally feasible. One common approach is to employ the Reynolds-averaged Navier-Stokes (RANS) formulation, which requires a model to represent the Reynolds stresses. Existing models are justified on the basis of observations and asymptotic results for simple turbulent flows and assume a universal behavior. This introduces epistemic uncertainty. An alternative route explored more recently is to develop data-driven Reynolds stress representations using machine learning tools. However, often these models also fail to generalize due to the limited training data. Steerable E(3) Equivariant Graph Neural Networks (SEGNNs) offer a promising solution by improving generalization without requiring data augmentation. SEGNNs naturally align with CFD mesh structures, integrate equivariance to retain the natural representation and properties of physical quantities in vector or matrix forms and incorporate attention mechanisms to include non-locality considerations. This work demonstrates the formulation and application of SEGNNs for fluid mechanics broadly, showcasing their potential to reduce uncertainty and enhance accuracy in relevant flow simulations.