# Super-resolving sparse observations in partial differential equations: A physics-constrained convolutional neural network approach

arXiv: https://arxiv.org/abs/2306.10990 · HTML: https://mlsanity.com/paper/2306.10990/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Jun 2023.

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

- [Physics-constrained convolutional neural networks for inverse problems in spatiotemporal partial differential equations](https://mlsanity.com/paper/2401.10306/) (2024)

## Abstract (arXiv)

We propose the physics-constrained convolutional neural network (PC-CNN) to infer the high-resolution solution from sparse observations of spatiotemporal and nonlinear partial differential equations. Results are shown for a chaotic and turbulent fluid motion, whose solution is high-dimensional, and has fine spatiotemporal scales. We show that, by constraining prior physical knowledge in the CNN, we can infer the unresolved physical dynamics without using the high-resolution dataset in the training. This opens opportunities for super-resolution of experimental data and low-resolution simulations.