Shallow neural networks for fluid flow reconstruction with limited sensors. (24th June 2020)

• Record Type: Journal Article
• Authors: Erichson, N. Benjamin; Mathelin, Lionel; Yao, Zhewei; Brunton, Steven L.; Mahoney, Michael W.; Kutz, J. Nathan
• Is Part Of: Proceedings. Volume 476:Number 2238(2020)
• Publication Date: 2020-06-24
• Subjects: neural networks -- sensors -- flow field estimation -- fluid dynamics -- machine learning; Physical sciences -- Periodicals; Engineering -- Periodicals; Mathematics -- Periodicals; 500
• DOI: 10.1098/rspa.2020.0097
• Languages: English
• ISSNs: 1364-5021

Abstract

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 to 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.