A Gaussian Process Regression approach within a data-driven POD framework for engineering problems in fluid dynamics

Giulio Ortali; Nicola Demo; Gianluigi Rozza; Giulio Ortali; Nicola Demo; Gianluigi Rozza

doi:10.3934/mine.2022021

Mathematics in Engineering

2022, Volume 4, Issue 3: 1-16. doi: 10.3934/mine.2022021

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Research article

A Gaussian Process Regression approach within a data-driven POD framework for engineering problems in fluid dynamics

1.
Mathematics Area, mathLab, SISSA, via Bonomea 265, I-34136 Trieste, Italy
2.
Department of Applied Physics, Eindhoven University of Technology, The Netherlands

Received: 22 November 2020 Accepted: 20 July 2021 Published: 06 August 2021

This work describes the implementation of a data-driven approach for the reduction of the complexity of parametrical partial differential equations (PDEs) employing Proper Orthogonal Decomposition (POD) and Gaussian Process Regression (GPR). This approach is applied initially to a literature case, the simulation of the Stokes problem, and in the following to a real-world industrial problem, within a shape optimization pipeline for a naval engineering problem.
- data-driven method,
- reduced order modeling,
- Gaussian Process Regression,
- parametric design problem
Citation: Giulio Ortali, Nicola Demo, Gianluigi Rozza. A Gaussian Process Regression approach within a data-driven POD framework for engineering problems in fluid dynamics[J]. Mathematics in Engineering, 2022, 4(3): 1-16. doi: 10.3934/mine.2022021

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Abstract

This work describes the implementation of a data-driven approach for the reduction of the complexity of parametrical partial differential equations (PDEs) employing Proper Orthogonal Decomposition (POD) and Gaussian Process Regression (GPR). This approach is applied initially to a literature case, the simulation of the Stokes problem, and in the following to a real-world industrial problem, within a shape optimization pipeline for a naval engineering problem.

References

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