An Operator Learning Framework for Spatiotemporal Super-resolution of Scientific Simulations

Abstract

In numerous contexts, high-resolution solutions to partial differential equations are required to capture faithfully essential dynamics which occur at small spatiotemporal scales, but these solutions can be very difficult and slow to obtain using traditional methods due to limited computational resources. A recent direction to circumvent these computational limitations is to use machine learning techniques for super-resolution, to reconstruct high-resolution numerical solutions from low-resolution simulations which can be obtained more efficiently. The proposed approach, the Super Resolution Operator Network (SROpNet), frames super-resolution as an operator learning problem and draws inspiration from existing architectures to learn continuous representations of solutions to parametric differential equations from low-resolution approximations, which can then be evaluated at any desired location. In addition, no restrictions are imposed on the locations of (the fixed number of) spatiotemporal sensors at which the low-resolution approximations are provided, thereby enabling the consideration of a broader spectrum of problems arising in practice, for which many existing super-resolution approaches are not well-suited.