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

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.Comment: Supplementary Video: https://youtu.be/mjqwPch9gDo. Accepted to SC2

Mini-Workshop: Numerical Upscaling for Flow Problems: Theory and Applications

The objective of this workshop was to bring together researchers working in multiscale simulations with emphasis on multigrid methods and multiscale finite element methods, aiming at chieving of better understanding and synergy between these methods. The goal of multiscale finite element methods, as upscaling methods, is to compute coarse scale solutions of the underlying equations as accurately as possible. On the other hand, multigrid methods attempt to solve fine-scale equations rapidly using a hierarchy of coarse spaces. Multigrid methods need “good” coarse scale spaces for their efficiency. The discussions of this workshop partly focused on approximation properties of coarse scale spaces and multigrid convergence. Some other presentations were on upscaling, domain decomposition methods and nonlinear multiscale methods. Some researchers discussed applications of these methods to reservoir simulations, as well as to simulations of filtration, insulating materials, and turbulence