A GENERIC-guided active learning SPH method for viscoelastic fluids using Gaussian process regression

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Main Authors: Dong, Xuekai, Simavilla, David Nieto, Ouyang, Jie, Wang, Xiaodong, Ellero, Marco
Format: Preprint
Published: 2025
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_version_ 1866913914864795648
author Dong, Xuekai
Simavilla, David Nieto
Ouyang, Jie
Wang, Xiaodong
Ellero, Marco
author_facet Dong, Xuekai
Simavilla, David Nieto
Ouyang, Jie
Wang, Xiaodong
Ellero, Marco
contents When applying machine learning methods to learn viscoelastic constitutive relations, the polymer history dependence in viscoelastic fluids and the generalization ability of machine learning models are challenging. In this paper, guided by the general equation for nonequilibrium reversible-irreversible coupling (GENERIC) framework, a novel GENERIC-guided active learning smoothed particle hydrodynamics (${\rm{G^2ALSPH}}$) method is proposed to obtain effective constitutive relations for reliable simulations of viscoelastic flows. By utilizing the GENERIC framework, the target viscoelastic constitutive relation is reduced to a simple functional relation between the eigenvalues of the conformation tensor and the eigenvalues of its thermodynamically conjugated tensorial variable, which incorporates the flow-history-dependent memory effect. Based on data and Gaussian process regression (GPR), a new active learning strategy is developed to obtain the simplified constitutive relation, in which the generalization ability is ensured by actively acquiring more data points when needed. Moreover, a novel relative uncertainty is devised to establish an accuracy evaluation tool for the GPR prediction results, which reduces the number of required training data points while maintaining accuracy. Furthermore, the SPH method combined with the latest techniques serves as an effective macroscopic numerical method. Eventually, the Poiseuille flows and the flows around a periodic array of cylinders at different Weissenberg numbers are simulated to validate the effectiveness and accuracy of the ${\rm{G^2ALSPH}}$ method. The Oldroyd-B model is used as the ground truth constitutive relation to provide data for GPR, bringing analytical solutions for comparison. The excellent performance demonstrates that the ${\rm{G^2ALSPH}}$ method has promising applications in data-driven simulations of viscoelastic fluids.
format Preprint
id arxiv_https___arxiv_org_abs_2506_21877
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle A GENERIC-guided active learning SPH method for viscoelastic fluids using Gaussian process regression
Dong, Xuekai
Simavilla, David Nieto
Ouyang, Jie
Wang, Xiaodong
Ellero, Marco
Fluid Dynamics
Computational Physics
When applying machine learning methods to learn viscoelastic constitutive relations, the polymer history dependence in viscoelastic fluids and the generalization ability of machine learning models are challenging. In this paper, guided by the general equation for nonequilibrium reversible-irreversible coupling (GENERIC) framework, a novel GENERIC-guided active learning smoothed particle hydrodynamics (${\rm{G^2ALSPH}}$) method is proposed to obtain effective constitutive relations for reliable simulations of viscoelastic flows. By utilizing the GENERIC framework, the target viscoelastic constitutive relation is reduced to a simple functional relation between the eigenvalues of the conformation tensor and the eigenvalues of its thermodynamically conjugated tensorial variable, which incorporates the flow-history-dependent memory effect. Based on data and Gaussian process regression (GPR), a new active learning strategy is developed to obtain the simplified constitutive relation, in which the generalization ability is ensured by actively acquiring more data points when needed. Moreover, a novel relative uncertainty is devised to establish an accuracy evaluation tool for the GPR prediction results, which reduces the number of required training data points while maintaining accuracy. Furthermore, the SPH method combined with the latest techniques serves as an effective macroscopic numerical method. Eventually, the Poiseuille flows and the flows around a periodic array of cylinders at different Weissenberg numbers are simulated to validate the effectiveness and accuracy of the ${\rm{G^2ALSPH}}$ method. The Oldroyd-B model is used as the ground truth constitutive relation to provide data for GPR, bringing analytical solutions for comparison. The excellent performance demonstrates that the ${\rm{G^2ALSPH}}$ method has promising applications in data-driven simulations of viscoelastic fluids.
title A GENERIC-guided active learning SPH method for viscoelastic fluids using Gaussian process regression
topic Fluid Dynamics
Computational Physics
url https://arxiv.org/abs/2506.21877