# Shallow Neural Networks for Fluid Flow Reconstruction with Limited Sensors

## TL;DR

This paper introduces a shallow neural network approach for reconstructing fluid flow fields from limited sensor data, outperforming traditional methods and requiring fewer sensors, suitable for global monitoring with sparse measurements.

## Contribution

The paper presents a novel shallow neural network methodology for fluid flow reconstruction that is data-driven, end-to-end, and requires no prior knowledge or heavy preprocessing.

## Key findings

- Outperforms traditional modal approximation techniques.
- Achieves comparable performance with fewer sensors.
- Effective in fluid mechanics and oceanography applications.

## Abstract

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.