Physics-guided surrogate models for fluid dynamics in complex geometries*

Data-driven surrogate models based on deep learning have been shown to predict spatiotemporal dynamics orders of magnitude faster than traditional solvers. While much work on spatiotemporal  surrogate models has dealt with canonical problems on gridded domains, many real-world problems involve complex geometry that may only be represented accurately through modern geometric deep learning approaches. Furthermore, pure data-driven surrogate models often fail to pertain to the underlying physical laws of the system. We propose a novel implementation of SO(3)-equivariant tensor convolutional networks to model moderate Reynolds number fluid systems in an arbitrary point-cloud domain. We use our model to predict turbulent quantities such as the Reynolds stresses and to forecast the velocity field with dynamics represented by a NeuralODE framework. Our model integrates physics principles by encoding symmetries in the architecture design. The efficacy of the encoded symmetries is validated with equivariance error and generalization to different geometries. This work aims to significantly expand  the problem domain of deep learning surrogate models, contributing towards more efficient scientific modeling techniques in complex geometries.