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Hammering at the entropy: a GENERIC-guided approach to learning polymeric rheological constitutive equations using PINNs

David Nieto Simavilla Orcid Logo, Andrea Bonfanti, Imanol García-Beristain, Pep Español, Marco Ellero

Journal of Fluid Mechanics, Volume: 1016, Start page: A11

Swansea University Author: Marco Ellero

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DOI (Published version): 10.1017/jfm.2025.10325

Abstract

We present a versatile framework that employs Physics-Informed Neural Networks (PINNs) to discover the entropic contribution that leads to the constitutive equation for the extra-stress in rheological models of dilute polymer solutions. In this framework the training of the neural network is guided...

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Published in: Journal of Fluid Mechanics
ISSN: 0022-1120 1469-7645
Published: Cambridge University Press (CUP) 2025
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URI: https://cronfa.swan.ac.uk/Record/cronfa70050
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spelling 2025-07-29T13:11:28.3910408 v2 70050 2025-07-29 Hammering at the entropy: a GENERIC-guided approach to learning polymeric rheological constitutive equations using PINNs 84f2af0791d38bdbf826728de7e5c69d Marco Ellero Marco Ellero true false 2025-07-29 We present a versatile framework that employs Physics-Informed Neural Networks (PINNs) to discover the entropic contribution that leads to the constitutive equation for the extra-stress in rheological models of dilute polymer solutions. In this framework the training of the neural network is guided by an evolution equation for the conformation tensor, which is GENERIC-compliant. We compare two training methodologies for the data-driven PINN constitutive models: one trained on data from the analytical solution of the Oldroyd-B (OB) model under steady-state rheometric flows (PINN-rheometric), and another trained on in silico data generated from computational fluid dynamics (CFD) simulations of complex flow around a cylinder that use the OB model (PINN-complex). The capacity of the PINN models to provide good predictions is evaluated by comparison with CFD simulations using the underlying OB model as a reference. Both models are capable of predicting flow behaviour in transient and complex conditions; however, the PINN-complex model, trained on a broader range of mixed-flow data, outperforms the PINN-rheometric model in complex flow scenarios. The geometry agnostic character of our methodology allows us to apply the learned PINN models to flows with topologies different from those used for training. Journal Article Journal of Fluid Mechanics 1016 A11 Cambridge University Press (CUP) 0022-1120 1469-7645 rheology, viscoelasticity, non-Newtonian flows 10 8 2025 2025-08-10 10.1017/jfm.2025.10325 COLLEGE NANME COLLEGE CODE Swansea University Another institution paid the OA fee This research is supported by the Basque Government through the BERC 2022-2025 program, the ELKARTEK 2022 and 2024 programs (KAIROS project: grant KK-2022/00052 and ELASTBAT: KK-2024/00091). The research is also partially funded by the Spanish State Research Agency through BCAM Severo Ochoa excellence accreditation CEX2021-0011 42-S/MICIN/AEI/10.13039/501100011033, and through projects PID2020-117080RB-C55 (‘Microscopic foundations of soft-matter experiments: computational nano-hydrodynamics’ and acronym ‘Compu-Nano-Hydro’) and PID2020-117080RB-C54 (‘Coarse-Graining theory and experimental techniques for multiscale biological systems’) funded by AEI – MICIN. 2025-07-29T13:11:28.3910408 2025-07-29T12:59:10.1035307 Faculty of Science and Engineering School of Engineering and Applied Sciences - Chemical Engineering David Nieto Simavilla 0000-0001-5389-4827 1 Andrea Bonfanti 2 Imanol García-Beristain 3 Pep Español 4 Marco Ellero 5 70050__34856__e6dd116e8eb94a2090641cc49f6299f9.pdf S002211202510325Xa.pdf 2025-07-29T12:59:10.0859993 Output 2827995 application/pdf Version of Record true © The Author(s), 2025. This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (CC BY). true eng https://creativecommons.org/licenses/by/4.0/
title Hammering at the entropy: a GENERIC-guided approach to learning polymeric rheological constitutive equations using PINNs
spellingShingle Hammering at the entropy: a GENERIC-guided approach to learning polymeric rheological constitutive equations using PINNs
Marco Ellero
title_short Hammering at the entropy: a GENERIC-guided approach to learning polymeric rheological constitutive equations using PINNs
title_full Hammering at the entropy: a GENERIC-guided approach to learning polymeric rheological constitutive equations using PINNs
title_fullStr Hammering at the entropy: a GENERIC-guided approach to learning polymeric rheological constitutive equations using PINNs
title_full_unstemmed Hammering at the entropy: a GENERIC-guided approach to learning polymeric rheological constitutive equations using PINNs
title_sort Hammering at the entropy: a GENERIC-guided approach to learning polymeric rheological constitutive equations using PINNs
author_id_str_mv 84f2af0791d38bdbf826728de7e5c69d
author_id_fullname_str_mv 84f2af0791d38bdbf826728de7e5c69d_***_Marco Ellero
author Marco Ellero
author2 David Nieto Simavilla
Andrea Bonfanti
Imanol García-Beristain
Pep Español
Marco Ellero
format Journal article
container_title Journal of Fluid Mechanics
container_volume 1016
container_start_page A11
publishDate 2025
institution Swansea University
issn 0022-1120
1469-7645
doi_str_mv 10.1017/jfm.2025.10325
publisher Cambridge University Press (CUP)
college_str Faculty of Science and Engineering
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hierarchy_top_id facultyofscienceandengineering
hierarchy_top_title Faculty of Science and Engineering
hierarchy_parent_id facultyofscienceandengineering
hierarchy_parent_title Faculty of Science and Engineering
department_str School of Engineering and Applied Sciences - Chemical Engineering{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Engineering and Applied Sciences - Chemical Engineering
document_store_str 1
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description We present a versatile framework that employs Physics-Informed Neural Networks (PINNs) to discover the entropic contribution that leads to the constitutive equation for the extra-stress in rheological models of dilute polymer solutions. In this framework the training of the neural network is guided by an evolution equation for the conformation tensor, which is GENERIC-compliant. We compare two training methodologies for the data-driven PINN constitutive models: one trained on data from the analytical solution of the Oldroyd-B (OB) model under steady-state rheometric flows (PINN-rheometric), and another trained on in silico data generated from computational fluid dynamics (CFD) simulations of complex flow around a cylinder that use the OB model (PINN-complex). The capacity of the PINN models to provide good predictions is evaluated by comparison with CFD simulations using the underlying OB model as a reference. Both models are capable of predicting flow behaviour in transient and complex conditions; however, the PINN-complex model, trained on a broader range of mixed-flow data, outperforms the PINN-rheometric model in complex flow scenarios. The geometry agnostic character of our methodology allows us to apply the learned PINN models to flows with topologies different from those used for training.
published_date 2025-08-10T05:21:30Z
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