A model hierarchy for predicting the flow in stirred tanks with physics-informed neural networks
This paper explores the potential of Physics-Informed Neural Networks (PINNs) to serve as Reduced Order Models (ROMs) for simulating the flow field within stirred tank reactors (STRs). We solve the two-dimensional stationary Navier-Stokes equations within a geometrically intricate domain and explore...
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| Vydané v: | Advances in Computational Science and Engineering Ročník 2; číslo 2; s. 91 - 129 |
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| Jazyk: | English |
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01.06.2024
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| ISSN: | 2837-1739, 2837-1739 |
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| Abstract | This paper explores the potential of Physics-Informed Neural Networks (PINNs) to serve as Reduced Order Models (ROMs) for simulating the flow field within stirred tank reactors (STRs). We solve the two-dimensional stationary Navier-Stokes equations within a geometrically intricate domain and explore methodologies that allow us to integrate additional physical insights into the model. These approaches include imposing the Dirichlet boundary conditions (BCs) strongly and employing domain decomposition (DD), with both overlapping and non-overlapping subdomains. We adapt the Extended Physics-Informed Neural Network (XPINN) approach to solve different sets of equations in distinct subdomains based on the diverse flow characteristics present in each region. Our exploration results in a hierarchy of models spanning various levels of complexity, where the best models exhibit $ \ell_1 $ prediction errors of less than 1% for both pressure and velocity. To illustrate the reproducibility of our approach, we track the errors over repeated independent training runs of the best identified model and show its reliability. Subsequently, by incorporating the stirring rate as a parametric input, we develop a fast-to-evaluate model of the flow capable of interpolating across a wide range of Reynolds numbers. Although we exclusively restrict ourselves to STRs in this work, we conclude that the steps taken to obtain the presented model hierarchy can be transferred to other applications. |
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| AbstractList | This paper explores the potential of Physics-Informed Neural Networks (PINNs) to serve as Reduced Order Models (ROMs) for simulating the flow field within stirred tank reactors (STRs). We solve the two-dimensional stationary Navier-Stokes equations within a geometrically intricate domain and explore methodologies that allow us to integrate additional physical insights into the model. These approaches include imposing the Dirichlet boundary conditions (BCs) strongly and employing domain decomposition (DD), with both overlapping and non-overlapping subdomains. We adapt the Extended Physics-Informed Neural Network (XPINN) approach to solve different sets of equations in distinct subdomains based on the diverse flow characteristics present in each region. Our exploration results in a hierarchy of models spanning various levels of complexity, where the best models exhibit $ \ell_1 $ prediction errors of less than 1% for both pressure and velocity. To illustrate the reproducibility of our approach, we track the errors over repeated independent training runs of the best identified model and show its reliability. Subsequently, by incorporating the stirring rate as a parametric input, we develop a fast-to-evaluate model of the flow capable of interpolating across a wide range of Reynolds numbers. Although we exclusively restrict ourselves to STRs in this work, we conclude that the steps taken to obtain the presented model hierarchy can be transferred to other applications. |
| Author | Wolff, Daniel Elgeti, Stefanie von Lieres, Eric Trávníková, Veronika Behr, Marek Dirkes, Nico |
| Author_xml | – sequence: 1 givenname: Veronika surname: Trávníková fullname: Trávníková, Veronika email: travnikova@cats.rwth-aachen.de organization: Chair for Computational Analysis of Technical Systems, RWTH Aachen University, Germany – sequence: 2 givenname: Daniel surname: Wolff fullname: Wolff, Daniel email: d.wolff@unibw.de organization: Chair for Computational Analysis of Technical Systems, RWTH Aachen University, Germany – sequence: 3 givenname: Nico surname: Dirkes fullname: Dirkes, Nico email: dirkes@aices.rwth-aachen.de organization: Chair for Computational Analysis of Technical Systems, RWTH Aachen University, Germany – sequence: 4 givenname: Stefanie surname: Elgeti fullname: Elgeti, Stefanie email: stefanie.elgeti@tuwien.ac.at organization: Institute for Lightweight Design and Structural Biomechanics, TU Wien, Austria – sequence: 5 givenname: Eric surname: von Lieres fullname: von Lieres, Eric email: e.von.lieres@fz-juelich.de organization: Institute of Bio- and Geosciences 1: Biotechnology, Forschungszentrum Jülich, Germany – sequence: 6 givenname: Marek surname: Behr fullname: Behr, Marek email: behr@cats.rwth-aachen.de organization: Chair for Computational Analysis of Technical Systems, RWTH Aachen University, Germany |
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| Cites_doi | 10.4208/cicp.oa-2020-0164 10.1016/j.jcp.2020.110085 10.1016/0045-7825(92)90059-S 10.1007/s10915-022-01939-z 10.1007/s10409-021-01148-1 10.1016/j.cma.2019.112623 10.1016/j.jcp.2018.10.045 10.1016/j.cma.2024.116979 10.3390/e24091254 10.1007/s10444-023-10065-9 10.1137/19M1274067 10.1063/5.0095270 10.1145/279232.279236 10.1142/S0218213020500098 10.1016/j.jcp.2021.110768 10.1016/j.neucom.2020.09.006 10.1137/20M1318043 10.1063/5.0180770 10.3390/w13040423 10.1016/j.commatsci.2020.110187 10.3389/fphy.2020.00042 10.1002/pamm.202300203 10.1038/s41592-020-0772-5 10.1016/j.jsv.2021.116196 10.1126/science.aaw4741 10.1177/0954410019890721 10.1016/j.cma.2019.112732 10.1021/acs.jpca.3c06265 10.1002/aic.690381003 10.1016/j.ces.2018.05.008 10.1016/j.jcp.2021.110683 10.1016/j.cma.2021.113741 10.1016/j.cam.2021.113887 10.1137/0916069 10.1016/j.jcp.2020.109951 10.1109/72.712178 10.1186/s40323-024-00265-3 10.1016/j.cma.2020.113028 10.1016/j.jcp.2022.111402 10.1016/j.cma.2022.115810 |
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| Keywords | stirred tank reactors domain decomposition Physics-informed neural networks reduced order modeling Navier-Stokes equations |
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