Volume 1, Issue 1
DeePN$^2$: A Deep Learning-Based Non-Newtonian Hydrodynamic Model

Lidong Fang, Pei Ge, Lei Zhang, Weinan E & Huan Lei

J. Mach. Learn. , 1 (2022), pp. 114-140.

Published online: 2022-03

Primary Category: Application; Secondary Category: Algorithm

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  • Abstract

A long standing problem in the modeling of non-Newtonian hydrodynamics of polymeric flows is the availability of reliable and interpretable hydrodynamic models that faithfully encode the underlying microscale polymer dynamics. The main complication arises from the long polymer relaxation time, the complex molecular structure and heterogeneous interaction. DeePN$^2,$ a deep learning-based non-Newtonian hydrodynamic model, has been proposed and has shown some success in systematically passing the micro-scale structural mechanics information to the macro-scale hydrodynamics for suspensions with simple polymer conformation and bond potential. The model retains a multi-scaled nature by mapping the polymer configurations into a set of symmetry-preserving macro-scale features. The extended constitutive laws for these macro-scale features can be directly learned from the kinetics of their micro-scale counterparts. In this paper, we develop DeePN$^2$ using more complex micro-structural models. We show that DeePN$^2$ can faithfully capture the broadly overlooked viscoelastic differences arising from the specific molecular structural mechanics without human intervention.

  • General Summary

Developing reliable physical models for the macro-scale hydrodynamics of non-Newtonian fluids has remained a challenging task for many decades. This study presents a deep learning-based non-Newtonian hydrodynamic model, DeePN$^2$, for constructing accurate and interpretable models directly from micro-scale descriptions. Molecular-level fidelity is retained by mapping the polymer configurations into a set of symmetry-preserving macro-scale features. The extended constitutive laws for these macro-scale features, including a new form of the objective tensor derivative, can be directly learned from the kinetics of their micro-scale counterparts. The construction is end-to-end and strictly preserves physical symmetries. It is demonstrated that DeePN$^2$ can faithfully capture the broadly overlooked viscoelastic differences arising from the specific molecular structural mechanics without human intervention.  

  • Keywords

Non-Newtonian fluids, Machine learning, Multi-scale modeling, Fluid mechanics.

  • AMS Subject Headings

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COPYRIGHT: © Global Science Press

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@Article{JML-1-114, author = {Lidong and Fang and and 22784 and and Lidong Fang and Pei and Ge and and 22785 and and Pei Ge and Lei and Zhang and and 22786 and and Lei Zhang and Weinan and E and and 22787 and and Weinan E and Huan and Lei and and 22788 and and Huan Lei}, title = {DeePN$^2$: A Deep Learning-Based Non-Newtonian Hydrodynamic Model}, journal = {Journal of Machine Learning}, year = {2022}, volume = {1}, number = {1}, pages = {114--140}, abstract = {

A long standing problem in the modeling of non-Newtonian hydrodynamics of polymeric flows is the availability of reliable and interpretable hydrodynamic models that faithfully encode the underlying microscale polymer dynamics. The main complication arises from the long polymer relaxation time, the complex molecular structure and heterogeneous interaction. DeePN$^2,$ a deep learning-based non-Newtonian hydrodynamic model, has been proposed and has shown some success in systematically passing the micro-scale structural mechanics information to the macro-scale hydrodynamics for suspensions with simple polymer conformation and bond potential. The model retains a multi-scaled nature by mapping the polymer configurations into a set of symmetry-preserving macro-scale features. The extended constitutive laws for these macro-scale features can be directly learned from the kinetics of their micro-scale counterparts. In this paper, we develop DeePN$^2$ using more complex micro-structural models. We show that DeePN$^2$ can faithfully capture the broadly overlooked viscoelastic differences arising from the specific molecular structural mechanics without human intervention.

}, issn = {2790-2048}, doi = {https://doi.org/10.4208/jml.220115}, url = {http://global-sci.org/intro/article_detail/jml/20373.html} }
TY - JOUR T1 - DeePN$^2$: A Deep Learning-Based Non-Newtonian Hydrodynamic Model AU - Fang , Lidong AU - Ge , Pei AU - Zhang , Lei AU - E , Weinan AU - Lei , Huan JO - Journal of Machine Learning VL - 1 SP - 114 EP - 140 PY - 2022 DA - 2022/03 SN - 1 DO - http://doi.org/10.4208/jml.220115 UR - https://global-sci.org/intro/article_detail/jml/20373.html KW - Non-Newtonian fluids, Machine learning, Multi-scale modeling, Fluid mechanics. AB -

A long standing problem in the modeling of non-Newtonian hydrodynamics of polymeric flows is the availability of reliable and interpretable hydrodynamic models that faithfully encode the underlying microscale polymer dynamics. The main complication arises from the long polymer relaxation time, the complex molecular structure and heterogeneous interaction. DeePN$^2,$ a deep learning-based non-Newtonian hydrodynamic model, has been proposed and has shown some success in systematically passing the micro-scale structural mechanics information to the macro-scale hydrodynamics for suspensions with simple polymer conformation and bond potential. The model retains a multi-scaled nature by mapping the polymer configurations into a set of symmetry-preserving macro-scale features. The extended constitutive laws for these macro-scale features can be directly learned from the kinetics of their micro-scale counterparts. In this paper, we develop DeePN$^2$ using more complex micro-structural models. We show that DeePN$^2$ can faithfully capture the broadly overlooked viscoelastic differences arising from the specific molecular structural mechanics without human intervention.

Lidong Fang, Pei Ge, Lei Zhang, Weinan E & Huan Lei. (2022). DeePN$^2$: A Deep Learning-Based Non-Newtonian Hydrodynamic Model. Journal of Machine Learning. 1 (1). 114-140. doi:10.4208/jml.220115
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