# Reconstructing Rayleigh-Benard flows out of temperature-only measurements using Physics-Informed Neural Networks

arXiv: https://arxiv.org/abs/2301.07769 · HTML: https://mlsanity.com/paper/2301.07769/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 41 references that are in the map.
- First posted on arXiv 18 Jan 2023.

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

- [Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains](https://mlsanity.com/paper/2006.10739/) (2020)
- [Scientific Machine Learning through Physics-Informed Neural Networks: Where we are and What's next](https://mlsanity.com/paper/2201.05624/) (2022)
- [Physics-informed neural networks (PINNs) for fluid mechanics: A review](https://mlsanity.com/paper/2105.09506/) (2021)
- [Physics-informed neural network for ultrasound nondestructive quantification of surface breaking cracks](https://mlsanity.com/paper/2005.03596/) (2020)
- [Physics-informed neural networks for solving Reynolds-averaged Navierunicodex2013Stokes equations](https://mlsanity.com/paper/2107.10711/) (2021)
- [Physics-informed deep-learning applications to experimental fluid mechanics](https://mlsanity.com/paper/2203.15402/) (2022)
- [Reconstruction of turbulent data with deep generative models for semantic inpainting from TURB-Rot database](https://mlsanity.com/paper/2006.09179/) (2020)
- [Downscaling the 2D Benard Convection Equations Using Continuous Data Assimilation](https://mlsanity.com/paper/1512.04671/) (2015)

## Built on by (most cited first, 2 of 2)

- [From PINNs to PIKANs: Recent Advances in Physics-Informed Machine Learning](https://mlsanity.com/paper/2410.13228/) (2024)
- [Surrogate Modeling of 3D Rayleigh-Benard Convection with Equivariant Autoencoders](https://mlsanity.com/paper/2505.13569/) (2025)

## Abstract (arXiv)

We investigate the capabilities of Physics-Informed Neural Networks (PINNs) to reconstruct turbulent Rayleigh-Benard flows using only temperature information. We perform a quantitative analysis of the quality of the reconstructions at various amounts of low-passed-filtered information and turbulent intensities. We compare our results with those obtained via nudging, a classical equation-informed data assimilation technique. At low Rayleigh numbers, PINNs are able to reconstruct with high precision, comparable to the one achieved with nudging. At high Rayleigh numbers, PINNs outperform nudging and are able to achieve satisfactory reconstruction of the velocity fields only when data for temperature is provided with high spatial and temporal density. When data becomes sparse, the PINNs performance worsens, not only in a point-to-point error sense but also, and contrary to nudging, in a statistical sense, as can be seen in the probability density functions and energy spectra.