MeshfreeFlowNet: a physics-constrained deep continuous space-time super-resolution framework

We propose MeshfreeFlowNet, a novel deep learningbased super-resolution framework to generate continuous (grid-free) spatio-temporal solutions from the low-resolution inputs. While being computationally efficient, Mesh-freeFlowNet 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 Mesh-freeFlowNet on the task of super-resolution of turbulent flows in the Rayleigh-Bénard convection problem. Across a diverse set of evaluation metrics, we show that Mesh-freeFlowNet 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.

We provide an open-source implementation of our method that supports arbitrary combinations of PDE constraints 1 .