Neural Differential Equations for Single Image Super-Resolution

Teven Le Scao

Keywords: Neural Differential Equations, Image super-resolution, Total variation methods, partial differential equations

TL;DR: We test Neural differential equations on image super-resolution to learn a PDE that solves the task instead of finding it with a heuristic, and benchmark Neural DEs on a real-world task in the process.

Abstract: Although Neural Differential Equations have shown promise on toy problems such as MNIST, they have yet to be successfully applied to more challenging tasks. Inspired by variational methods for image restoration relying on partial differential equations, we choose to benchmark several forms of Neural DEs and backpropagation methods on single image super-resolution. The adjoint method previously proposed for gradient estimation has no theoretical stability guarantees; we find a practical case where this makes it unusable, and show that discrete sensitivity analysis has better stability. In our experiments, differential models match the performance of a state-of-the art super-resolution model.

Community Implementations: [ 1 code implementation](https://www.catalyzex.com/paper/arxiv:2005.00865/code)