MeshfreeFlowNet: A Physics-Constrained Deep Continuous Space-Time Super-Resolution Framework

Chiyu "Max" Jiang*      Soheil Esmaeilzadeh*      Kamyar Azizzadenesheli      Karthik Kashinath       Mustafa Mustafa      Hamdi Tchelepi     Philip Marcus     Prabhat     Anima Anandkumar
(* Denotes Equal Contributions)

[Paper]  [Code]  [Bibtex]  [Video]

Figure 1 MeshfreeFlowNet is a novel deep learning-based super-resolution framework to generate continuous (grid-free) spatio-temporal solutions from the low-resolution inputs. It consists of two end-to-end trainable modules, the Context Generation Network, and a Continuous Decoding Network.

Abstract

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–Bénard 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.

Figure 2 Visualization of the super-resolution quality of the MeshfreeFlowNet. The framerate is limitted for the gif animation. For better results, checkout the video link above.