Extrapolating fluid dynamics with spatiotemporal convolution networks

There is a critical need for efficient and reliable active flow control strategies to reduce drag and noise in various engineering systems. While traditional full-order models based on the Navier-Stokes equations are not feasible, advanced model reduction techniques can be inefficient for active control tasks, especially with strong nonlinearity and convection-dominated phenomena. In our recent works, deep learning-based surrogate models have been shown to be effective and they run orders of magnitude faster than full-order simulations. However, outside of the training data, these models encounter significant challenges, limiting their effectiveness in real-world applications. In this study, we aim to improve the extrapolation capability of deep neural networks by modifying the network architecture and integrating physics as an implicit bias. Surrogate models via deep learning generally employ decoupling in spatial and temporal dimensions, which can introduce modelling and approximation errors. To alleviate these errors, we propose a novel technique for learning coupled spatial-temporal correlation using total convolution networks. We compare the proposed technique against a standard encoder-propagator-decoder model and demonstrate a superior extrapolation performance.