# An Operator Learning Framework for Spatiotemporal Super-resolution of Scientific Simulations

arXiv: https://arxiv.org/abs/2311.02328 · HTML: https://mlsanity.com/paper/2311.02328/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 67 of its 112 references that are in the map.
- First posted on arXiv 4 Nov 2023.

## Builds on (most cited first, 30 of 67)

- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators](https://mlsanity.com/paper/1910.03193/) (2019)
- [Photo-Realistic Single Image Super-Resolution Using a Generative Adversarial Network](https://mlsanity.com/paper/1609.04802/) (2016)
- [Enhanced Deep Residual Networks for Single Image Super-Resolution](https://mlsanity.com/paper/1707.02921/) (2017)
- [Image Super-Resolution Using Very Deep Residual Channel Attention Networks](https://mlsanity.com/paper/1807.02758/) (2018)
- [ESRGAN: Enhanced Super-Resolution Generative Adversarial Networks](https://mlsanity.com/paper/1809.00219/) (2018)
- [Image Super-Resolution Using Deep Convolutional Networks](https://mlsanity.com/paper/1501.00092/) (2014)
- [Accurate Image Super-Resolution Using Very Deep Convolutional Networks](https://mlsanity.com/paper/1511.04587/) (2015)
- [GradNorm: Gradient Normalization for Adaptive Loss Balancing in Deep Multitask Networks](https://mlsanity.com/paper/1711.02257/) (2017)
- [Residual Dense Network for Image Super-Resolution](https://mlsanity.com/paper/1802.08797/) (2018)
- [Characterizing possible failure modes in physics-informed neural networks](https://mlsanity.com/paper/2109.01050/) (2021)
- [When and why PINNs fail to train: A neural tangent kernel perspective](https://mlsanity.com/paper/2007.14527/) (2020)
- [Video Enhancement with Task-Oriented Flow](https://mlsanity.com/paper/1711.09078/) (2017)
- [DeepXDE: A deep learning library for solving differential equations](https://mlsanity.com/paper/1907.04502/) (2019)
- [Physics-Informed Neural Operator for Learning Partial Differential Equations](https://mlsanity.com/paper/2111.03794/) (2021)
- [EDVR: Video Restoration with Enhanced Deformable Convolutional Networks](https://mlsanity.com/paper/1905.02716/) (2019)
- [Physics-informed neural networks (PINNs) for fluid mechanics: A review](https://mlsanity.com/paper/2105.09506/) (2021)
- [Deep Laplacian Pyramid Networks for Fast and Accurate Super-Resolution](https://mlsanity.com/paper/1704.03915/) (2017)
- [Fourier Neural Operator with Learned Deformations for PDEs on General Geometries](https://mlsanity.com/paper/2207.05209/) (2022)
- [SRDiff: Single Image Super-Resolution with Diffusion Probabilistic Models](https://mlsanity.com/paper/2104.14951/) (2021)
- [Neural Operator: Learning Maps Between Function Spaces](https://mlsanity.com/paper/2108.08481/) (2021)
- [Accelerating the Super-Resolution Convolutional Neural Network](https://mlsanity.com/paper/1608.00367/) (2016)
- [Physics Informed Deep Learning (Part I): Data-driven Solutions of Nonlinear Partial Differential Equations](https://mlsanity.com/paper/1711.10561/) (2017)
- [Deep Learning for Image Super-resolution: A Survey](https://mlsanity.com/paper/1902.06068/) (2019)
- [B-PINNs: Bayesian Physics-Informed Neural Networks for Forward and Inverse PDE Problems with Noisy Data](https://mlsanity.com/paper/2003.06097/) (2020)
- [Geometry-Informed Neural Operator for Large-Scale 3D PDEs](https://mlsanity.com/paper/2309.00583/) (2023)
- [U-FNO -- An enhanced Fourier neural operator-based deep-learning model for multiphase flow](https://mlsanity.com/paper/2109.03697/) (2021)
- [Transformer for Partial Differential Equations' Operator Learning](https://mlsanity.com/paper/2205.13671/) (2022)
- [Fast, Accurate, and Lightweight Super-Resolution with Cascading Residual Network](https://mlsanity.com/paper/1803.08664/) (2018)
- [Model Reduction and Neural Networks for Parametric PDEs](https://mlsanity.com/paper/2005.03180/) (2020)

## Abstract (arXiv)

In numerous contexts, high-resolution solutions to partial differential equations are required to capture faithfully essential dynamics which occur at small spatiotemporal scales, but these solutions can be very difficult and slow to obtain using traditional methods due to limited computational resources. A recent direction to circumvent these computational limitations is to use machine learning techniques for super-resolution, to reconstruct high-resolution numerical solutions from low-resolution simulations which can be obtained more efficiently. The proposed approach, the Super Resolution Operator Network (SROpNet), frames super-resolution as an operator learning problem and draws inspiration from existing architectures to learn continuous representations of solutions to parametric differential equations from low-resolution approximations, which can then be evaluated at any desired location. In addition, no restrictions are imposed on the locations of (the fixed number of) spatiotemporal sensors at which the low-resolution approximations are provided, thereby enabling the consideration of a broader spectrum of problems arising in practice, for which many existing super-resolution approaches are not well-suited.