POD-Galerkin reduced order models and physics-informed neural networks for solving inverse problems for the Navier-Stokes equations
- We present a Reduced Order Model (ROM) which exploits recent developments in Physics Informed Neural Networks (PINNs) for solving inverse problems for the Navier-Stokes equations (NSE). In the proposed approach, the presence of simulated data for the fluid dynamics fields is assumed. A POD-Galerkin ROM is then constructed by applying POD on the snapshots matrices of the fluid fields and performing a Galerkin projection of the NSE (or the modified equations in case of turbulence modeling) onto the POD reduced basis. A POD-Galerkin PINN ROM is then derived by introducing deep neural networks which approximate the reduced outputs with the input being time and/or parameters of the model. The neural networks incorporate the physical equations (the POD-Galerkin reduced equations) into their structure as part of the loss function. Using this approach, the reduced model is able to approximate unknown parameters such as physical constants or the boundary conditions. A demonstration of the applicability of the proposed ROM is illustrated byWe present a Reduced Order Model (ROM) which exploits recent developments in Physics Informed Neural Networks (PINNs) for solving inverse problems for the Navier-Stokes equations (NSE). In the proposed approach, the presence of simulated data for the fluid dynamics fields is assumed. A POD-Galerkin ROM is then constructed by applying POD on the snapshots matrices of the fluid fields and performing a Galerkin projection of the NSE (or the modified equations in case of turbulence modeling) onto the POD reduced basis. A POD-Galerkin PINN ROM is then derived by introducing deep neural networks which approximate the reduced outputs with the input being time and/or parameters of the model. The neural networks incorporate the physical equations (the POD-Galerkin reduced equations) into their structure as part of the loss function. Using this approach, the reduced model is able to approximate unknown parameters such as physical constants or the boundary conditions. A demonstration of the applicability of the proposed ROM is illustrated by three cases which are the steady flow around a backward step, the flow around a circular cylinder and the unsteady turbulent flow around a surface mounted cubic obstacle.…
Verfasserangaben: | Saddam HijaziORCiD, Melina A. FreitagORCiDGND, Niels LandwehrORCiDGND |
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DOI: | https://doi.org/10.1186/s40323-023-00242-2 |
ISSN: | 2213-7467 |
Titel des übergeordneten Werks (Englisch): | Advanced modeling and simulation in engineering sciences : AMSES |
Verlag: | SpringerOpen |
Verlagsort: | Berlin |
Publikationstyp: | Wissenschaftlicher Artikel |
Sprache: | Englisch |
Datum der Erstveröffentlichung: | 18.03.2023 |
Erscheinungsjahr: | 2023 |
Datum der Freischaltung: | 21.06.2024 |
Freies Schlagwort / Tag: | Inverse problems; Navier-Stokes equations; Physics-based machine learning; Proper orthogonal decomposition |
Band: | 10 |
Ausgabe: | 1 |
Aufsatznummer: | 5 |
Seitenanzahl: | 38 |
Fördernde Institution: | Projekt DEAL; Jacobi Fellowship at the University of Potsdam; Deutsche; Forschungsgemeinschaft (DFG) [318763901 -SFB1294] |
Organisationseinheiten: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Mathematik |
DDC-Klassifikation: | 0 Informatik, Informationswissenschaft, allgemeine Werke / 00 Informatik, Wissen, Systeme / 000 Informatik, Informationswissenschaft, allgemeine Werke |
5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik | |
Peer Review: | Referiert |
Publikationsweg: | Open Access / Gold Open-Access |
DOAJ gelistet | |
Lizenz (Deutsch): | ![]() |