  We propose MeshfreeFlowNet, 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, MeshfreeFlowNet
accurately recovers the fine-scale quantities of interest. MeshfreeFlowNet
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 MeshfreeFlowNet 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 MeshfreeFlowNet significantly outperforms
existing baselines. Furthermore, we provide a large scale implementation of
MeshfreeFlowNet and show that it efficiently scales across large clusters,
achieving 96.80% scaling efficiency on up to 128 GPUs and a training time of
less than 4 minutes.
