Super Resolution Based on Deep Operator Networks

TL;DR

This paper demonstrates that Deep Operator Networks can effectively perform super-resolution reconstruction of PDE solutions, outperforming traditional interpolation methods in accuracy, especially in capturing high-frequency details and small-scale structures.

Contribution

The paper introduces the application of DeepONets to super-resolution of PDE solutions, incorporating convolutional layers for efficiency, and compares its performance with conventional interpolation methods.

Findings

DeepONets accurately predict high-frequency oscillations.

DeepONets outperform cubic spline interpolation in accuracy.

Convolutional layers reduce computational cost in 2D problems.

Abstract

We use Deep Operator Networks (DeepONets) to perform super-resolution reconstruction of the solutions of two types of partial differential equations and compare the model predictions with the results obtained using conventional interpolation methods to verify the advantages of DeepONets. We employ two pooling methods to downsample the origin data and conduct super-resolution reconstruction under three different resolutions of input images. The results show that the DeepONet model can predict high-frequency oscillations and small-scale structures from low-resolution inputs very well. For the two-dimensional problem, we introduce convolutional layers to extract information from input images at a lower cost than purer MLPs. We adjust the size of the training set and observe the variation of prediction errors. In both one-dimensional and two-dimensional cases, the super-resolution reconstruction using the DeepONet model demonstrates much more accurate prediction results than cubic spline interpolation, highlighting the superiority of operator learning methods in handling such problems compared to traditional interpolation techniques.