# Multiscale Corrections by Continuous Super-Resolution

arXiv: https://arxiv.org/abs/2411.07576 · HTML: https://mlsanity.com/paper/2411.07576/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 39 of its 84 references that are in the map.
- First posted on arXiv 12 Nov 2024.

## Builds on (most cited first, 30 of 39)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [3D Gaussian Splatting for Real-Time Radiance Field Rendering](https://mlsanity.com/paper/2308.04079/) (2023)
- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [Implicit Neural Representations with Periodic Activation Functions](https://mlsanity.com/paper/2006.09661/) (2020)
- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [Photo-Realistic Single Image Super-Resolution Using a Generative Adversarial Network](https://mlsanity.com/paper/1609.04802/) (2016)
- [SwinIR: Image Restoration Using Swin Transformer](https://mlsanity.com/paper/2108.10257/) (2021)
- [Image Super-Resolution via Iterative Refinement](https://mlsanity.com/paper/2104.07636/) (2021)
- [Image Super-Resolution Using Deep Convolutional Networks](https://mlsanity.com/paper/1501.00092/) (2014)
- [Learning Implicit Fields for Generative Shape Modeling](https://mlsanity.com/paper/1812.02822/) (2018)
- [Residual Dense Network for Image Super-Resolution](https://mlsanity.com/paper/1802.08797/) (2018)
- [Convolutional Occupancy Networks](https://mlsanity.com/paper/2003.04618/) (2020)
- [Differentiable Volumetric Rendering: Learning Implicit 3D Representations without 3D Supervision](https://mlsanity.com/paper/1912.07372/) (2019)
- [Learning Continuous Image Representation with Local Implicit Image Function](https://mlsanity.com/paper/2012.09161/) (2020)
- [Exploiting Diffusion Prior for Real-World Image Super-Resolution](https://mlsanity.com/paper/2305.07015/) (2023)
- [Local Implicit Grid Representations for 3D Scenes](https://mlsanity.com/paper/2003.08981/) (2020)
- [Single Image Super-Resolution via a Holistic Attention Network](https://mlsanity.com/paper/2008.08767/) (2020)
- [Model Reduction and Neural Networks for Parametric PDEs](https://mlsanity.com/paper/2005.03180/) (2020)
- [Spherical Fourier Neural Operators: Learning Stable Dynamics on the Sphere](https://mlsanity.com/paper/2306.03838/) (2023)
- [WIRE: Wavelet Implicit Neural Representations](https://mlsanity.com/paper/2301.05187/) (2023)
- [Implicit Diffusion Models for Continuous Super-Resolution](https://mlsanity.com/paper/2303.16491/) (2023)
- [Texture Fields: Learning Texture Representations in Function Space](https://mlsanity.com/paper/1905.07259/) (2019)
- [Meta-SR: A Magnification-Arbitrary Network for Super-Resolution](https://mlsanity.com/paper/1903.00875/) (2019)
- [PhyGeoNet: Physics-Informed Geometry-Adaptive Convolutional Neural Networks for Solving Parameterized Steady-State PDEs on Irregular Domain](https://mlsanity.com/paper/2004.13145/) (2020)
- [BACON: Band-limited Coordinate Networks for Multiscale Scene Representation](https://mlsanity.com/paper/2112.04645/) (2021)
- [Beyond Periodicity: Towards a Unifying Framework for Activations in Coordinate-MLPs](https://mlsanity.com/paper/2111.15135/) (2021)
- [Local Texture Estimator for Implicit Representation Function](https://mlsanity.com/paper/2111.08918/) (2021)
- [VideoINR: Learning Video Implicit Neural Representation for Continuous Space-Time Super-Resolution](https://mlsanity.com/paper/2206.04647/) (2022)
- [A Theoretical Analysis of Deep Neural Networks and Parametric PDEs](https://mlsanity.com/paper/1904.00377/) (2019)
- [CiaoSR: Continuous Implicit Attention-in-Attention Network for Arbitrary-Scale Image Super-Resolution](https://mlsanity.com/paper/2212.04362/) (2022)

## Built on by (most cited first, 1 of 1)

- [MCMC Informed Neural Emulators for Uncertainty Quantification in Dynamical Systems](https://mlsanity.com/paper/2603.10987/) (2026)

## Abstract (arXiv)

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.