A Deep Learning Based Physics Informed Continuous Spatio Temporal Super-Resolution Framework

We propose a novel deep learning based super-resolution framework to generate continuous (grid-free) spatio-temporal solutions from the low-resolution inputs. While being computationally efficient, our proposed framework accurately recovers the fine-scale quantities of interest and allows for: (i) the output to be sampled at all spatio-temporal resolutions, (ii) a set of Partial Differential Equation (PDE) constraints to be imposed, and (iii) training on fixed-size inputs on arbitrarily sized spatio-temporal domains owing to its fully convolutional encoder. We empirically study the performance of our framework on the task of super-resolution of turbulent flows in the Rayleigh-Benard convection problem. Across a diverse set of evaluation metrics, we show that our proposed framework significantly outperforms the existing baselines. Furthermore, we provide a large-scale implementation of our framework and show that it efficiently scales across large clusters, achieving 96.80 percent scaling efficiency on up to 128 GPUs and a training time of less than 4 minutes. We provide an open-source implementation of our method that supports arbitrary combinations of PDE constraints.