Towards Physics-informed Deep Learning for Spatiotemporal Modeling of Turbulent Flows

Simulating the spatio-temporal evolution of a complex physical system over a realistic domain (eg. GCMs for climate) is extremely compute-intensive with current PDE-solver based numerical approaches. Data-driven methods, such as deep learning, are beginning to show promise for augmenting or even replacing compute-intensive parts of computational physics models, such as climate and weather models. However, it remains a grand challenge to incorporate physical principles in a systematic manner to the design, training and inference of such models. Physics informed deep learning aims to infuse principles governing the dynamics of physical systems into data-driven deep learning models, but existing studies are either limited to linear dynamics or spatial constraints of physical systems.

In this paper, we study the challenging task of spatiotemporal modeling of velocity fields for a highly nonlinear turbulent flow. We conduct comprehensive experiments and evaluations for various state-of- the-art physics informed deep learning methods, including purely data-driven models and physics-informed models. We benchmark these methods on the task of forecasting velocity fields at different future time horizons, given historic data of different lengths. We also provide valuable technical insights for these techniques. We find that incorporating prior physics knowledge can not only speed up the training process but improve model performance. Our results show that the Spatiotemporal Generative Networks with an autoregressive U-net as the generator performs the best for varying forecasting horizons consistently performs the best for varying forecasting horizon.