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Hammering at the entropy: a GENERIC-guided approach to learning polymeric rheological constitutive equations using PINNs
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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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© The Author(s), 2025. This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (CC BY).
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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...
| Published in: | Journal of Fluid Mechanics |
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| ISSN: | 0022-1120 1469-7645 |
| Published: |
Cambridge University Press (CUP)
2025
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| Online Access: |
Check full text
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| URI: | https://cronfa.swan.ac.uk/Record/cronfa70050 |
| 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 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. |
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| Keywords: |
rheology, viscoelasticity, non-Newtonian flows |
| College: |
Faculty of Science and Engineering |
| Funders: |
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. |
| Start Page: |
A11 |