DeepM&amp;Mnet: Inferring the electroconvection multiphysics fields based on operator approximation by neural networks

Cai, Shengze; Wang, Zhicheng; Lu, Lu; Zaki, Tamer A.; Karniadakis, George Em

doi:10.1016/j.jcp.2021.110296

DeepM&Mnet: Inferring the electroconvection multiphysics fields based on operator approximation by neural networks

Journal Article · Mon Mar 22 00:00:00 EDT 2021 · Journal of Computational Physics

DOI:https://doi.org/10.1016/j.jcp.2021.110296· OSTI ID:2282980

Cai, Shengze ^[1]; Wang, Zhicheng ^[2]; ^[3]; Zaki, Tamer A. ^[4]; Karniadakis, George Em ^[2]

Brown University, Providence, RI (United States); Brown University
Brown University, Providence, RI (United States)
Massachusetts Institute of Technology (MIT), Cambridge, MA (United States)
Johns Hopkins University, Baltimore, MD (United States)

Electroconvection is a multiphysics problem involving coupling of the flow field with the electric field as well as the cation and anion concentration fields. Here, we use electroconvection as a benchmark problem to put forward a new data assimilation framework, the DeepM&Mnet, for simulating multiphysics and multiscale problems at speeds much faster than standard numerical methods using pre-trained neural networks. We first pre-train DeepONets that can predict independently each field, given general inputs from the rest of the fields of the coupled system. DeepONets can approximate nonlinear operators and are composed of two sub-networks, a branch net for the input fields and a trunk net for the locations of the output field. DeepONets, which are extremely fast, are used as building blocks in the DeepM&Mnet and form constraints for the multiphysics solution along with some sparse available measurements of any of the fields. We demonstrate the new methodology and document the accuracy of each individual DeepONet, and subsequently we present two different DeepM&Mnet architectures that infer accurately and efficiently 2D electroconvection fields for unseen electric potentials. Furthermore, the DeepM&Mnet framework is general and can be applied for building any complex multiphysics and multiscale models based on very few measurements using pre-trained DeepONets in a “plug-and-play” mode.

View Accepted Manuscript (DOE)

Research Organization:: Brown University, Providence, RI (United States)

Sponsoring Organization:: USDOE

Grant/Contract Number:: SC0019453

OSTI ID:: 2282980

Alternate ID(s):: OSTI ID: 1782341
OSTI ID: 23206097

Journal Information:: Journal of Computational Physics, Journal Name: Journal of Computational Physics Vol. 436; ISSN 0021-9991

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

References (44)

Electro-osmotic slip and electroconvective instability Zaltzman, B.; Rubinstein, I. Journal of Fluid Mechanics, Vol. 579 https://doi.org/10.1017/s0022112007004880	journal	May 2007
Electro-osmotically induced convection at a permselective membrane Rubinstein, I.; Zaltzman, B. Physical Review E, Vol. 62, Issue 2 https://doi.org/10.1103/physreve.62.2238	journal	August 2000
Statistical analysis of electroconvection near an ion-selective membrane in the highly chaotic regime Druzgalski, Clara; Mani, Ali Physical Review Fluids, Vol. 1, Issue 7 https://doi.org/10.1103/physrevfluids.1.073601	journal	November 2016
Direct Observation of a Nonequilibrium Electro-Osmotic Instability Rubinstein, S. M.; Manukyan, G.; Staicu, A. Physical Review Letters, Vol. 101, Issue 23 https://doi.org/10.1103/physrevlett.101.236101	journal	December 2008
Coupling between Buoyancy Forces and Electroconvective Instability near Ion-Selective Surfaces Karatay, Elif; Andersen, Mathias Bækbo; Wessling, Matthias Physical Review Letters, Vol. 116, Issue 19 https://doi.org/10.1103/physrevlett.116.194501	journal	May 2016
Dense motion estimation of particle images via a convolutional neural network Cai, Shengze; Zhou, Shichao; Xu, Chao Experiments in Fluids, Vol. 60, Issue 4 https://doi.org/10.1007/s00348-019-2717-2	journal	March 2019
Prediction of aerodynamic flow fields using convolutional neural networks Bhatnagar, Saakaar; Afshar, Yaser; Pan, Shaowu Computational Mechanics, Vol. 64, Issue 2 https://doi.org/10.1007/s00466-019-01740-0	journal	June 2019
Multilayer feedforward networks are universal approximators Hornik, Kurt; Stinchcombe, Maxwell; White, Halbert Neural Networks, Vol. 2, Issue 5 https://doi.org/10.1016/0893-6080(89)90020-8	journal	January 1989
Surrogate modeling for fluid flows based on physics-constrained deep learning without simulation data Sun, Luning; Gao, Han; Pan, Shaowu Computer Methods in Applied Mechanics and Engineering, Vol. 361 https://doi.org/10.1016/j.cma.2019.112732	journal	April 2020
Simulation of chaotic electrokinetic transport: Performance of commercial software versus custom-built direct numerical simulation codes Karatay, Elif; Druzgalski, Clara L.; Mani, Ali Journal of Colloid and Interface Science, Vol. 446 https://doi.org/10.1016/j.jcis.2014.12.081	journal	May 2015
DGM: A deep learning algorithm for solving partial differential equations Sirignano, Justin; Spiliopoulos, Konstantinos Journal of Computational Physics, Vol. 375 https://doi.org/10.1016/j.jcp.2018.08.029	journal	December 2018
Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations Raissi, M.; Perdikaris, P.; Karniadakis, G. E. Journal of Computational Physics, Vol. 378 https://doi.org/10.1016/j.jcp.2018.10.045	journal	February 2019
Physics-constrained deep learning for high-dimensional surrogate modeling and uncertainty quantification without labeled data Zhu, Yinhao; Zabaras, Nicholas; Koutsourelakis, Phaedon-Stelios Journal of Computational Physics, Vol. 394 https://doi.org/10.1016/j.jcp.2019.05.024	journal	October 2019
Discrete adjoint of fractional-step incompressible Navier-Stokes solver in curvilinear coordinates and application to data assimilation Wang, Mengze; Wang, Qi; Zaki, Tamer A. Journal of Computational Physics, Vol. 396 https://doi.org/10.1016/j.jcp.2019.06.065	journal	November 2019
Quantifying total uncertainty in physics-informed neural networks for solving forward and inverse stochastic problems Zhang, Dongkun; Lu, Lu; Guo, Ling Journal of Computational Physics, Vol. 397 https://doi.org/10.1016/j.jcp.2019.07.048	journal	November 2019
Kriging-enhanced ensemble variational data assimilation for scalar-source identification in turbulent environments Mons, Vincent; Wang, Qi; Zaki, Tamer A. Journal of Computational Physics, Vol. 398 https://doi.org/10.1016/j.jcp.2019.07.054	journal	December 2019
PDE-Net 2.0: Learning PDEs from data with a numeric-symbolic hybrid deep network Long, Zichao; Lu, Yiping; Dong, Bin Journal of Computational Physics, Vol. 399 https://doi.org/10.1016/j.jcp.2019.108925	journal	December 2019
NSFnets (Navier-Stokes flow nets): Physics-informed neural networks for the incompressible Navier-Stokes equations Jin, Xiaowei; Cai, Shengze; Li, Hui Journal of Computational Physics, Vol. 426 https://doi.org/10.1016/j.jcp.2020.109951	journal	February 2021
Electro-osmotic slip and electroconvective instability Zaltzman, B.; Rubinstein, I. Journal of Fluid Mechanics, Vol. 579 https://doi.org/10.1017/S0022112007004880	journal	May 2007
Reynolds averaged turbulence modelling using deep neural networks with embedded invariance Ling, Julia; Kurzawski, Andrew; Templeton, Jeremy Journal of Fluid Mechanics, Vol. 807 https://doi.org/10.1017/jfm.2016.615	journal	October 2016
Deep learning of vortex-induced vibrations Raissi, Maziar; Wang, Zhicheng; Triantafyllou, Michael S. Journal of Fluid Mechanics, Vol. 861 https://doi.org/10.1017/jfm.2018.872	journal	December 2018
Spatial reconstruction of steady scalar sources from remote measurements in turbulent flow Wang, Qi; Hasegawa, Yosuke; Zaki, Tamer A. Journal of Fluid Mechanics, Vol. 870 https://doi.org/10.1017/jfm.2019.241	journal	May 2019
Prediction of turbulent heat transfer using convolutional neural networks Kim, Junhyuk; Lee, Changhoon Journal of Fluid Mechanics, Vol. 882 https://doi.org/10.1017/jfm.2019.814	journal	November 2019
Learning nonlinear operators via DeepONet based on the universal approximation theorem of operators Lu, Lu; Jin, Pengzhan; Pang, Guofei Nature Machine Intelligence, Vol. 3, Issue 3 https://doi.org/10.1038/s42256-021-00302-5	journal	March 2021
Direct numerical simulation of electroconvective instability and hydrodynamic chaos near an ion-selective surface Druzgalski, C. L.; Andersen, M. B.; Mani, A. Physics of Fluids, Vol. 25, Issue 11 https://doi.org/10.1063/1.4818995	journal	November 2013
Operator learning for predicting multiscale bubble growth dynamics Lin, Chensen; Li, Zhen; Lu, Lu The Journal of Chemical Physics, Vol. 154, Issue 10 https://doi.org/10.1063/5.0041203	journal	March 2021
Solving high-dimensional partial differential equations using deep learning Han, Jiequn; Jentzen, Arnulf; E., Weinan Proceedings of the National Academy of Sciences, Vol. 115, Issue 34 https://doi.org/10.1073/pnas.1718942115	journal	August 2018
Reinforcement learning for bluff body active flow control in experiments and simulations Fan, Dixia; Yang, Liu; Wang, Zhicheng Proceedings of the National Academy of Sciences, Vol. 117, Issue 42 https://doi.org/10.1073/pnas.2004939117	journal	October 2020
Electro-osmotically induced convection at a permselective membrane Rubinstein, I.; Zaltzman, B. Physical Review E, Vol. 62, Issue 2 https://doi.org/10.1103/PhysRevE.62.2238	journal	August 2000
Helical vortex formation in three-dimensional electrochemical systems with ion-selective membranes Pham, Sang V.; Kwon, Hyuckjin; Kim, Bumjoo Physical Review E, Vol. 93, Issue 3 https://doi.org/10.1103/PhysRevE.93.033114	journal	March 2016
Statistical analysis of electroconvection near an ion-selective membrane in the highly chaotic regime Druzgalski, Clara; Mani, Ali Physical Review Fluids, Vol. 1, Issue 7 https://doi.org/10.1103/PhysRevFluids.1.073601	journal	November 2016
Direct Observation of a Nonequilibrium Electro-Osmotic Instability Rubinstein, S. M.; Manukyan, G.; Staicu, A. Physical Review Letters, Vol. 101, Issue 23 https://doi.org/10.1103/PhysRevLett.101.236101	journal	December 2008
Coupling between Buoyancy Forces and Electroconvective Instability near Ion-Selective Surfaces Karatay, Elif; Andersen, Mathias Bækbo; Wessling, Matthias Physical Review Letters, Vol. 116, Issue 19 https://doi.org/10.1103/PhysRevLett.116.194501	journal	May 2016
Approximations of continuous functionals by neural networks with application to dynamic systems Chen, T.; Chen, H. IEEE Transactions on Neural Networks, Vol. 4, Issue 6 https://doi.org/10.1109/72.286886	journal	January 1993
Universal approximation to nonlinear operators by neural networks with arbitrary activation functions and its application to dynamical systems No authors listed IEEE Transactions on Neural Networks, Vol. 6, Issue 4 https://doi.org/10.1109/72.392253	journal	July 1995
Data-driven discovery of partial differential equations Rudy, Samuel H.; Brunton, Steven L.; Proctor, Joshua L. Science Advances, Vol. 3, Issue 4 https://doi.org/10.1126/sciadv.1602614	journal	April 2017
Hidden fluid mechanics: Learning velocity and pressure fields from flow visualizations Raissi, Maziar; Yazdani, Alireza; Karniadakis, George Em Science, Vol. 367, Issue 6481 https://doi.org/10.1126/science.aaw4741	journal	January 2020
fPINNs: Fractional Physics-Informed Neural Networks Pang, Guofei; Lu, Lu; Karniadakis, George Em SIAM Journal on Scientific Computing, Vol. 41, Issue 4 https://doi.org/10.1137/18M1229845	journal	January 2019
DeepXDE: A Deep Learning Library for Solving Differential Equations Lu, Lu; Meng, Xuhui; Mao, Zhiping SIAM Review, Vol. 63, Issue 1 https://doi.org/10.1137/19M1274067	journal	January 2021
Turbulence Modeling in the Age of Data Duraisamy, Karthik; Iaccarino, Gianluca; Xiao, Heng Annual Review of Fluid Mechanics, Vol. 51, Issue 1 https://doi.org/10.1146/annurev-fluid-010518-040547	journal	January 2019
Machine Learning for Fluid Mechanics Brunton, Steven L.; Noack, Bernd R.; Koumoutsakos, Petros Annual Review of Fluid Mechanics, Vol. 52, Issue 1 https://doi.org/10.1146/annurev-fluid-010719-060214	journal	September 2019
Electroconvection Near Electrochemical Interfaces: Experiments, Modeling, and Computation Mani, Ali; Wang, Karen May Annual Review of Fluid Mechanics, Vol. 52, Issue 1 https://doi.org/10.1146/annurev-fluid-010719-060358	journal	January 2020
Physics-informed neural networks for inverse problems in nano-optics and metamaterials Chen, Yuyao; Lu, Lu; Karniadakis, George Em Optics Express, Vol. 28, Issue 8 https://doi.org/10.1364/OE.384875	journal	January 2020
Systems biology informed deep learning for inferring parameters and hidden dynamics Yazdani, Alireza; Lu, Lu; Raissi, Maziar PLOS Computational Biology, Vol. 16, Issue 11 https://doi.org/10.1371/journal.pcbi.1007575	journal	November 2020

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