Hostname: page-component-586b7cd67f-vdxz6 Total loading time: 0 Render date: 2024-11-23T14:01:10.108Z Has data issue: false hasContentIssue false
  • English
  • Français

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: [email protected]
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Aarts, D.G.A.L., Schmidt, M. & Lekkerkerker, H.N.W. 2004 Direct visual observation of thermal capillary waves. Science 304 (5672), 847–850.CrossRefGoogle ScholarPubMed
Abada, S., Marlair, G., Lecocq, A., Petit, M., Sauvant-Moynot, V. & Huet, F. 2016 Safety focused modeling of lithium-ion batteries: a review. J. Power Sources 306, 178–192.CrossRefGoogle Scholar
Arienti, M., Pan, W., Li, X. & Karniadakis, G.E. 2011 Many-body dissipative particle dynamics simulation of liquid/vapor and liquid/solid interactions. J. Chem. Phys. 134 (20), 204114.CrossRefGoogle ScholarPubMed
Baidakov, V.G. & Protsenko, K.R. 2020 Molecular dynamics simulation of cavitation in a Lennard-Jones liquid at negative pressures. Chem. Phys. Lett. 760, 138030.CrossRefGoogle Scholar
Budarapu, P.R., Javvaji, B., Reinoso, J., Paggi, M. & Rabczuk, T. 2018 A three dimensional adaptive multiscale method for crack growth in silicon. Theor. Appl. Fract. Mec. 96, 576–603.CrossRefGoogle Scholar
Chen, T. & Chen, H. 1995 Universal approximation to nonlinear operators by neural networks with arbitrary activation functions and its application to dynamical systems. IEEE Trans. Neural Netw. 6 (4), 911–917.CrossRefGoogle ScholarPubMed
Chen, C.J., Kuang, Y.D., Zhu, S.Z., Burgert, I., Keplinger, T., Gong, A., Li, T., Berglund, L., Eichhorn, S.J. & Hu, L.B. 2020 Structure-property-function relationships of natural and engineered wood. Nat. Rev. Mater. 5 (9), 642–666.CrossRefGoogle Scholar
Cheung, J., Frischknecht, A.L., Perego, M. & Bochev, P. 2017 A hybrid, coupled approach for modeling charged fluids from the nano to the mesoscale. J. Comput. Phys. 348, 364–384.CrossRefGoogle Scholar
Español, P. & Warren, P. 1995 Statistical mechanics of dissipative particle dynamics. Europhys. Lett. 30 (4), 191–196.CrossRefGoogle Scholar
Fedosov, D.A. & Karniadakis, G.E. 2009 Triple-decker: interfacing atomistic-mesoscopic-continuum flow regimes. J. Comput. Phys. 228 (4), 1157–1171.CrossRefGoogle Scholar
Fuster, D., Dopazo, C. & Hauke, G. 2011 Liquid compressibility effects during the collapse of a single cavitating bubble. J. Acoust. Soc. Am. 129 (1), 122–131.CrossRefGoogle ScholarPubMed
Ghahramani, E., Arabnejad, M. & Bensow, R.E. 2019 A comparative study between numerical methods in simulation of cavitating bubbles. Intl J. Multiphase Flow 111, 339–359.CrossRefGoogle Scholar
Goel, S., et al. 2020 Horizons of modern molecular dynamics simulation in digitalized solid freeform fabrication with advanced materials. Mater. Today Chem. 18, 100356.CrossRefGoogle Scholar
Gooneie, A., Schuschnigg, S. & Holzer, C. 2017 A review of multiscale computational methods in polymeric materials. Polymers 9 (1), 16.CrossRefGoogle ScholarPubMed
Groot, R.D. & Warren, P.B. 1997 Dissipative particle dynamics: bridging the gap between atomistic and mesoscopic simulation. J. Chem. Phys. 107 (11), 4423–4435.CrossRefGoogle Scholar
Hoogerbrugge, P.J. & Koelman, J. 1992 Simulating microscopic hydrodynamic phenomena with dissipative particle dynamics. Europhys. Lett. 19 (3), 155–160.CrossRefGoogle Scholar
Lin, C., Li, Z., Lu, L., Cai, S., Maxey, M. & Karniadakis, G.E. 2021 Operator learning for predicting multiscale bubble growth dynamics. J. Chem. Phys. 154 (10), 104118.CrossRefGoogle ScholarPubMed
Lu, L., Jin, P., Pang, G., Zhang, Z. & Karniadakis, G.E. 2021 a Learning nonlinear operators via DeepONet based on the universal approximation theorem of operators. Nat. Mach. Intell. 3 (3), 218–229.CrossRefGoogle Scholar
Lu, L., Meng, X., Mao, Z. & Karniadakis, G.E. 2021 b DeepXDE: A deep learning library for solving differential equations. SIAM Rev. 63 (1), 208–228.CrossRefGoogle Scholar
Maulik, R., Fukami, K., Ramachandra, N., Fukagata, K. & Taira, K. 2020 Probabilistic neural networks for fluid flow surrogate modeling and data recovery. Phys. Rev. Fluids 5 (10), 104401.CrossRefGoogle Scholar
Pagonabarraga, I. & Frenkel, D. 2001 Dissipative particle dynamics for interacting systems. J. Chem. Phys. 115 (11), 5015–5026.CrossRefGoogle Scholar
Pan, D., Zhao, G., Lin, Y. & Shao, X. 2018 Mesoscopic modelling of microbubble in liquid with finite density ratio of gas to liquid. Europhys. Lett. 122 (2), 20003.CrossRefGoogle Scholar
Peng, G.C., et al. 2021 Multiscale modeling meets machine learning: what can we learn? Arch. Comput. Meth. Engng 28, 1017–1037.CrossRefGoogle ScholarPubMed
Plesset, M.S. & Prosperetti, A. 1977 Bubble dynamics and cavitation. Annu. Rev. Fluid Mech. 9 (1), 145–185.CrossRefGoogle Scholar
Prosperetti, A. & Lezzi, A. 1986 Bubble dynamics in a compressible liquid. Part 1. First-order theory. J. Fluid Mech. 168, 457–478.CrossRefGoogle Scholar
Rycroft, C.H. 2009 VORO++: a three-dimensional voronoi cell library in C++. Chaos 19 (4), 041111.CrossRefGoogle ScholarPubMed
Tang, Y.-H., Kudo, S., Bian, X., Li, Z. & Karniadakis, G.E. 2015 Multiscale universal interface: A concurrent framework for coupling heterogeneous solvers. J. Comput. Phys. 297, 13–31.CrossRefGoogle Scholar
Wang, Q. 2014 Multi-oscillations of a bubble in a compressible liquid near a rigid boundary. J. Fluid Mech. 745, 509–536.CrossRefGoogle Scholar
Wang, Y., Li, Z., Xu, J., Yang, C. & Karniadakis, G.E. 2019 Concurrent coupling of atomistic simulation and mesoscopic hydrodynamics for flows over soft multi-functional surfaces. Soft Matt. 15 (8), 1747–1757.CrossRefGoogle ScholarPubMed
Warren, P.B. 2003 Vapor-liquid coexistence in many-body dissipative particle dynamics. Phys. Rev. E 68 (6), 066702.CrossRefGoogle ScholarPubMed
Yang, L., Meng, X. & Karniadakis, G.E. 2021 B-PINNs: Bayesian physics-informed neural networks for forward and inverse pde problems with noisy data. J. Comput. Phys. 425, 109913.CrossRefGoogle Scholar
Yip, S. & Short, M.P. 2013 Multiscale materials modelling at the mesoscale. Nat. Mater. 12 (9), 774–777.CrossRefGoogle Scholar
Zhao, Y., Xia, M. & Cao, Y. 2020 A study of bubble growth in the compressible Rayleigh–Taylor and Richtmyer–Meshkov instabilities. AIP Adv. 10 (1), 015056.CrossRefGoogle Scholar