Unifying Predictions of Deterministic and Stochastic Physics in Mesh-reduced Space with Sequential Flow Generative Model

Accurately predicting the physical dynamical systems in the unstructured mesh has recently gained much more attention in scientific AI fields. However, due to the complex physics of the underlying system, it is hard to use a unified framework to predict the behavior of both deterministic and stochastic systems. Moreover, there are challenges in predicting the solution in the original high-dimensional space. To bridge these gaps, we propose a framework with the regeneration learning paradigm for accurately predicting/generating fluid dynamics. Specifically, a novel graph auto-encoder is used to represent the full-space physical variables compactly in reduced space by projecting the high dimensional data into lower dimensional intrinsic space. Moreover, an attention-based sequence model is integrated into flow-based deep generative models to predict long time-dependent dynamics. The proposed model can accurately predict/generate several deterministic/stochastic fluid dynamics. Our model outperforms the competitive baseline models for deterministic systems, meanwhile providing a physical spatial-temporal pattern of forward uncertainty estimations. Moreover, our proposed model can generate different physical realizations of stochastic fluid dynamics systems, and the generated sample has high quality using different evaluation metrics.