Shallow neural networks for fluid flow reconstruction with limited sensors
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- N. Benjamin Erichson
- ICSI and Department of Statistics, University of California, Berkeley, Berkeley, CA, USA
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- Lionel Mathelin
- Université Paris-Saclay, CNRS, LIMSI, 91400 Orsay, France
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- Zhewei Yao
- Department of Mathematics, University of California, Berkeley, Berkeley, CA, USA
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- Steven L. Brunton
- Department of Mechanical Engineering, University of Washington, Seattle, WA, USA
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- Michael W. Mahoney
- ICSI and Department of Statistics, University of California, Berkeley, Berkeley, CA, USA
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- J. Nathan Kutz
- Department of Applied Mathematics, University of Washington, Seattle, WA, USA
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説明
<jats:p>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.</jats:p>
収録刊行物
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- Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
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Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 476 (2238), 20200097-, 2020-06
The Royal Society