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

From a numerical perspective, resolving the wide range of spatiotemporal scales within such physical systems is challenging since extremely small spatial and temporal numerical We propose MeshfreeFlowNet, a novel deep learningbased stencils would be required. In order to alleviate the super-resolution framework to generate continuous computational burden of fully resolving such a wide range (grid-free) spatiotemporal solutions from the low-resolution of spatial and temporal scales, multiscale computational approaches inputs. While being computationally efficient, MeshfreeFlowNet have been developed. For instance, in the subsurface accurately recovers the fine-scale quantities flow problem, the main idea of the multiscale approach of interest. MeshfreeFlowNet allows for: (i) the output is to build a set of operators that map between the unknowns to be sampled at all spatiotemporal resolutions, (ii) a set associated with the computational cells in a fine-grid and the of Partial Differential Equation (PDE) constraints to be imposed, unknowns on a coarser grid. The operators are computed and (iii) training on fixed-size inputs on arbitrarily numerically by solving localized flow problems. The multiscale sized spatiotemporal domains owing to its fully convolutional basis functions have subgrid-scale resolutions, ensuring encoder.