# Physics-Informed Neural Network Super Resolution for Advection-Diffusion Models

arXiv: https://arxiv.org/abs/2011.02519 · HTML: https://mlsanity.com/paper/2011.02519/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- Placed in Flow matching, time series and science, one of 14 directions in Diffusion models.
- Builds on 8 of its 22 references that are in the map.
- First posted on arXiv 4 Nov 2020.

## Placed in

- Diffusion models / [Flow matching, time series and science](https://mlsanity.com/diffusion/flow-matching-time-series-and-science/)

## Builds on (most cited first, 8 of 8)

- [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)
- [ESRGAN: Enhanced Super-Resolution Generative Adversarial Networks](https://mlsanity.com/paper/1809.00219/) (2018)
- [Accurate Image Super-Resolution Using Very Deep Convolutional Networks](https://mlsanity.com/paper/1511.04587/) (2015)
- [Deeply-Recursive Convolutional Network for Image Super-Resolution](https://mlsanity.com/paper/1511.04491/) (2015)
- [MemNet: A Persistent Memory Network for Image Restoration](https://mlsanity.com/paper/1708.02209/) (2017)
- [MeshfreeFlowNet: A Physics-Constrained Deep Continuous Space-Time Super-Resolution Framework](https://mlsanity.com/paper/2005.01463/) (2020)
- [Using Physics-Informed Super-Resolution Generative Adversarial Networks for Subgrid Modeling in Turbulent Reactive Flows](https://mlsanity.com/paper/1911.11380/) (2019)

## Built on by (most cited first, 16 of 16)

- [Physics-Informed Computer Vision: A Review and Perspectives](https://mlsanity.com/paper/2305.18035/) (2023)
- [SuperBench: A Super-Resolution Benchmark Dataset for Scientific Machine Learning](https://mlsanity.com/paper/2306.14070/) (2023)
- [Adversarial sampling of unknown and high-dimensional conditional distributions](https://mlsanity.com/paper/2111.05962/) (2021)
- [S3RP: Self-Supervised Super-Resolution and Prediction for Advection-Diffusion Process](https://mlsanity.com/paper/2111.04639/) (2021)
- [Physics-informed Deep Super-resolution for Spatiotemporal Data](https://mlsanity.com/paper/2208.01462/) (2022)
- [Representing Flow Fields with Divergence-Free Kernels for Reconstruction](https://mlsanity.com/paper/2504.01913/) (2025)
- [Rotationally Equivariant Super-Resolution of Velocity Fields in Two-Dimensional Fluids Using Convolutional Neural Networks](https://mlsanity.com/paper/2202.11099/) (2022)
- [Filtered Partial Differential Equations: a robust surrogate constraint in physics-informed deep learning framework](https://mlsanity.com/paper/2311.03776/) (2023)
- [Wasserstein GAN-Based Precipitation Downscaling with Optimal Transport for Enhancing Perceptual Realism](https://mlsanity.com/paper/2507.17798/) (2025)
- [Probabilistic Super-Resolution for Urban Micrometeorology via a Schr"odinger Bridge](https://mlsanity.com/paper/2510.12148/) (2025)
- [Physics-Informed Video Diffusion For Shallow Water Equations](https://mlsanity.com/paper/2603.15627/) (2026)
- [Tools for Extracting Spatio-Temporal Patterns in Meteorological Image Sequences: From Feature Engineering to Attention-Based Neural Networks](https://mlsanity.com/paper/2210.12310/) (2022)
- [Multi-task Learning for Source Attribution and Field Reconstruction for Methane Monitoring](https://mlsanity.com/paper/2211.00864/) (2022)
- [An Operator Learning Framework for Spatiotemporal Super-resolution of Scientific Simulations](https://mlsanity.com/paper/2311.02328/) (2023)
- [How to Re-enable PDE Loss for Physical Systems Modeling Under Partial Observation](https://mlsanity.com/paper/2412.09116/) (2024)
- [Atmos-Bench: 3D Atmospheric Structures for Climate Insight](https://mlsanity.com/paper/2507.11085/) (2025)

## Abstract (arXiv)

Physics-informed neural networks (NN) are an emerging technique to improve spatial resolution and enforce physical consistency of data from physics models or satellite observations. A super-resolution (SR) technique is explored to reconstruct high-resolution images (4×) from lower resolution images in an advection-diffusion model of atmospheric pollution plumes. SR performance is generally increased when the advection-diffusion equation constrains the NN in addition to conventional pixel-based constraints. The ability of SR techniques to also reconstruct missing data is investigated by randomly removing image pixels from the simulations and allowing the system to learn the content of missing data. Improvements in S/N of 11% are demonstrated when physics equations are included in SR with 40% pixel loss. Physics-informed NNs accurately reconstruct corrupted images and generate better results compared to the standard SR approaches.