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

Authors: Chiyu Jiang (University of California, Berkeley); Soheil Esmaeilzadeh (Stanford University); Kamyar Azizzadenesheli (California Institute of Technology); Karthik Kashinath and Mustafa Mustafa (Lawrence Berkeley National Laboratory); Hamdi A. Tchelepi (Stanford University); Philip S. Marcus (University of California, Berkeley); Mr Prabhat (Lawrence Berkeley National Laboratory); and Anima Anandkumar (California Institute of Technology, Nvidia Corporation)

Abstract: We propose MeshfreeFlowNet, a novel deep learning framework, to generate continuous (grid-free) spatiotemporal 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 spatiotemporal domains owing to its fully convolutional encoder.

We empirically study the performance of PCSR 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 PCSR significantly outperforms existing baselines. Furthermore, we provide a large scale implementation of PCSR 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.




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