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A seamless multiscale operator neural network for inferring bubble dynamics

Published online by Cambridge University Press:  21 October 2021

Chensen Lin Open the ORCID record for Chensen Lin [Opens in a new window] ,
Martin Maxey Open the ORCID record for Martin Maxey [Opens in a new window] ,
Zhen Li Open the ORCID record for Zhen Li [Opens in a new window]  and
George Em Karniadakis
Chensen Lin
Affiliation:
Division of Applied Mathematics, Brown University, Providence, RI 02912, USA
Martin Maxey
Affiliation:
Division of Applied Mathematics, Brown University, Providence, RI 02912, USA
Zhen Li
Affiliation:
Department of Mechanical Engineering, Clemson University, Clemson, SC 29634, USA
George Em Karniadakis*
Affiliation:
Division of Applied Mathematics, Brown University, Providence, RI 02912, USA School of Engineering, Brown University, Providence, RI 02912, USA
*
†Email address for correspondence: george_karniadakis@brown.edu
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Abstract

Modelling multiscale systems from nanoscale to macroscale requires the use of atomistic and continuum methods and, correspondingly, different computer codes. Here, we develop a seamless method based on DeepONet, which is a composite deep neural network (a branch and a trunk network) for regressing operators. In particular, we consider bubble growth dynamics, and we model tiny bubbles of initial size from 100 nm to 10 $\mathrm {\mu }\textrm {m}$, modelled by the Rayleigh–Plesset equation in the continuum regime above 1 $\mathrm {\mu }\textrm {m}$ and the dissipative particle dynamics method for bubbles below 1 $\mathrm {\mu }\textrm {m}$ in the atomistic regime. After an offline training based on data from both regimes, DeepONet can make accurate predictions of bubble growth on-the-fly (within a fraction of a second) across four orders of magnitude difference in spatial scales and two orders of magnitude in temporal scales. The framework of DeepONet is general and can be used for unifying physical models of different scales in diverse multiscale applications.

JFM classification

Mathematical Foundations: Machine learning Mathematical Foundations: Computational methods

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Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 929 , 25 December 2021 , A18
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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References

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