Multiscale corrections by continuous super-resolution.

Area of Science:

• Computational Science
• Artificial Intelligence
• Materials Science

Background:

• Finite element methods (FEM) often demand high resolution for accurate physical model approximation.
• Multiscale strategies can provide reasonable approximations on under-resolved scales, addressing FEM limitations.

Purpose of the Study:

• To propose a continuous super-resolution network using implicit neural representation for correcting multiscale effects in FEM.
• To enable accurate high-resolution predictions from coarse FEM data, both in-distribution and out-of-distribution.

Main Methods:

• Development of a local implicit transformer for learning multiscale features.
• Implementation of Gabor wavelet-based coordinate encodings to mitigate neural network bias towards low-frequency features.
• Utilization of stochastic cosine similarities for local feature comparison to enhance pattern supervision.

Main Results:

• The proposed network effectively learns multiscale features and provides superior in-distribution and out-of-distribution super-resolution.
• Gabor wavelet encodings improved the learning of high-frequency features.
• Stochastic cosine similarities enhanced structural alignment and local pattern accuracy.

Conclusions:

• The developed implicit neural representation strategy offers a powerful approach for super-resolution in finite element analysis.
• This method improves the accuracy and visual interpretability of results on under-resolved scales.
• The technique shows significant potential for advancing scientific visualization and analysis in computational modeling.