# Physics-Informed CNNs for Super-Resolution of Sparse Observations on Dynamical Systems

arXiv: https://arxiv.org/abs/2210.17319 · HTML: https://mlsanity.com/paper/2210.17319/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 16 references that are in the map.
- First posted on arXiv 31 Oct 2022.

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

- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [Visualizing the Loss Landscape of Neural Nets](https://mlsanity.com/paper/1712.09913/) (2017)
- [Accurate Image Super-Resolution Using Very Deep Convolutional Networks](https://mlsanity.com/paper/1511.04587/) (2015)
- [Physics-informed neural networks (PINNs) for fluid mechanics: A review](https://mlsanity.com/paper/2105.09506/) (2021)
- [Lagrangian Neural Networks](https://mlsanity.com/paper/2003.04630/) (2020)
- [Machine Learning for Fluid Mechanics](https://mlsanity.com/paper/1905.11075/) (2019)
- [Deep Learning for Single Image Super-Resolution: A Brief Review](https://mlsanity.com/paper/1808.03344/) (2018)
- [Physics-informed deep-learning applications to experimental fluid mechanics](https://mlsanity.com/paper/2203.15402/) (2022)

## Built on by (most cited first, 8 of 8)

- [Physics-Informed Computer Vision: A Review and Perspectives](https://mlsanity.com/paper/2305.18035/) (2023)
- [Reconstruction, forecasting, and stability of chaotic dynamics from partial data](https://mlsanity.com/paper/2305.15111/) (2023)
- [Multimodal Atmospheric Super-Resolution With Deep Generative Models](https://mlsanity.com/paper/2506.22780/) (2025)
- [Learning the solution operator of two-dimensional incompressible Navier-Stokes equations using physics-aware convolutional neural networks](https://mlsanity.com/paper/2308.02137/) (2023)
- [Thermodynamics-informed super-resolution of scarce temporal dynamics data](https://mlsanity.com/paper/2402.17506/) (2024)
- [Reconstructing unsteady flows from sparse, noisy measurements with a physics-constrained convolutional neural network](https://mlsanity.com/paper/2409.00260/) (2024)
- [How to Re-enable PDE Loss for Physical Systems Modeling Under Partial Observation](https://mlsanity.com/paper/2412.09116/) (2024)
- [Multimodal Spatiotemporal Atmospheric Data Assimilation with Latent Video Flow-matching](https://mlsanity.com/paper/2608.05103/) (2026)

## Abstract (arXiv)

In the absence of high-resolution samples, super-resolution of sparse observations on dynamical systems is a challenging problem with wide-reaching applications in experimental settings. We showcase the application of physics-informed convolutional neural networks for super-resolution of sparse observations on grids. Results are shown for the chaotic-turbulent Kolmogorov flow, demonstrating the potential of this method for resolving finer scales of turbulence when compared with classic interpolation methods, and thus effectively reconstructing missing physics.