Multiscale Corrections by Continuous Super-Resolution

TL;DR

This paper introduces a continuous super-resolution neural network with a local implicit transformer and Gabor wavelet encodings to improve multiscale finite element approximations, excelling in both in-distribution and out-of-distribution scenarios.

Contribution

It proposes a novel continuous super-resolution network with local implicit transformers and Gabor encodings for multiscale finite element correction, addressing low-frequency bias and local pattern supervision.

Findings

Achieves superior super-resolution performance on multiscale finite element data.

Effectively handles both in-distribution and out-of-distribution predictions.

Uses stochastic cosine similarities for better structural alignment.

Abstract

Finite element methods typically require a high resolution to satisfactorily approximate micro and even macro patterns of an underlying physical model. This issue can be circumvented by appropriate multiscale strategies that are able to obtain reasonable approximations on under-resolved scales. In this paper, we study the implicit neural representation and propose a continuous super-resolution network as a correction strategy for multiscale effects. It can take coarse finite element data to learn both in-distribution and out-of-distribution high-resolution finite element predictions. Our highlight is the design of a local implicit transformer, which is able to learn multiscale features. We also propose Gabor wavelet-based coordinate encodings, which can overcome the bias of neural networks learning low-frequency features. Finally, perception is often preferred over distortion, so scientists can recognize the visual pattern for further investigation. However, implicit neural representation is known for its lack of local pattern supervision. We propose to use stochastic cosine similarities to compare the local feature differences between prediction and ground truth. It shows better performance on structural alignments. Our experiments show that our proposed strategy achieves superior performance as an in-distribution and out-of-distribution super-resolution strategy.