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.

用机器学习技术进行超分辨率，从低分辨率模拟中重建高分辨率数值解的方法