Probabilistic surrogate modeling of unsteady fluid dynamics using deep graph normalizing flows

Surrogate modeling of spatiotemporal physics based on graph neural networks (GNN) has recently attracted increasing attention in the scientific machine learning community due to the flexibility of graphs in dealing with unstructured data. However, the model prediction often contains considerable uncertainty originated from data sparsity, noise, and model forms, which are critical in real-world applications but have yet been considered in existing works. In this work, we propose a novel probabilistic surrogate model, graph normalizing flows (GNF-Fluids), to accurately predict fluid dynamics with quantified uncertainties. Specifically, a novel message passing scheme is proposed to efficiently compute the Jacobian matrix in normalizing flows. A spatial encoder-decoder structure is constructed to compactly represent the flow fields in the mesh-reduced space. Moreover, an attention-based model is used for capturing long-term temporal structures. The proposed model is demonstrated on several complex flows, and the performance is compared with existing competitive state-of-the-art baseline models in terms of predictive accuracy and uncertainty quantification capability.