# Shallow Neural Networks for Fluid Flow Reconstruction with Limited Sensors

arXiv: https://arxiv.org/abs/1902.07358 · HTML: https://mlsanity.com/paper/1902.07358/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Feb 2019.

## Built on by (most cited first, 4 of 4)

- [State estimation with limited sensors -- A deep learning based approach](https://mlsanity.com/paper/2101.11513/) (2021)
- [SDYN-GANs: Adversarial Learning Methods for Multistep Generative Models for General Order Stochastic Dynamics](https://mlsanity.com/paper/2302.03663/) (2023)
- [Energy networks for state estimation with random sensors using sparse labels](https://mlsanity.com/paper/2203.06456/) (2022)
- [LC-SVD-DLinear: A low-cost physics-based hybrid machine learning model for data forecasting using sparse measurements](https://mlsanity.com/paper/2411.17433/) (2024)

## Abstract (arXiv)

In many applications, it is important to reconstruct a fluid flow field, or some other high-dimensional state, from limited measurements and limited data. In this work, we propose a shallow neural network-based learning methodology for such fluid flow reconstruction. Our approach learns an end-to-end mapping between the sensor measurements and the high-dimensional fluid flow field, without any heavy preprocessing on the raw data. No prior knowledge is assumed to be available, and the estimation method is purely data-driven. We demonstrate the performance on three examples in fluid mechanics and oceanography, showing that this modern data-driven approach outperforms traditional modal approximation techniques which are commonly used for flow reconstruction. Not only does the proposed method show superior performance characteristics, it can also produce a comparable level of performance with traditional methods in the area, using significantly fewer sensors. Thus, the mathematical architecture is ideal for emerging global monitoring technologies where measurement data are often limited.