Fed-DeepONet: Stochastic Gradient-Based Federated Training of Deep Operator Networks

The Deep Operator Network (DeepONet) framework is a different class of neural network architecture that one trains to learn nonlinear operators, i.e., mappings between infinite-dimensional spaces. Traditionally, DeepONets are trained using a centralized strategy that requires transferring the traini...

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Vydané v:	Algorithms Ročník 15; číslo 9; s. 325
Hlavní autori:	Moya, Christian, Lin, Guang
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	Basel MDPI AG 01.09.2022
Predmet:	Algorithms Analysis Clients Communication Computational linguistics Computer architecture Data security deep learning deep operator networks Digital twins Dynamic response Dynamical systems Engineering Experiments federated learning Language processing Natural language interfaces Neural networks Optimization Pendulums Privacy stochastic-gradient descent Training
ISSN:	1999-4893, 1999-4893
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Abstract	The Deep Operator Network (DeepONet) framework is a different class of neural network architecture that one trains to learn nonlinear operators, i.e., mappings between infinite-dimensional spaces. Traditionally, DeepONets are trained using a centralized strategy that requires transferring the training data to a centralized location. Such a strategy, however, limits our ability to secure data privacy or use high-performance distributed/parallel computing platforms. To alleviate such limitations, in this paper, we study the federated training of DeepONets for the first time. That is, we develop a framework, which we refer to as Fed-DeepONet, that allows multiple clients to train DeepONets collaboratively under the coordination of a centralized server. To achieve Fed-DeepONets, we propose an efficient stochastic gradient-based algorithm that enables the distributed optimization of the DeepONet parameters by averaging first-order estimates of the DeepONet loss gradient. Then, to accelerate the training convergence of Fed-DeepONets, we propose a moment-enhanced (i.e., adaptive) stochastic gradient-based strategy. Finally, we verify the performance of Fed-DeepONet by learning, for different configurations of the number of clients and fractions of available clients, (i) the solution operator of a gravity pendulum and (ii) the dynamic response of a parametric library of pendulums.
AbstractList	The Deep Operator Network (DeepONet) framework is a different class of neural network architecture that one trains to learn nonlinear operators, i.e., mappings between infinite-dimensional spaces. Traditionally, DeepONets are trained using a centralized strategy that requires transferring the training data to a centralized location. Such a strategy, however, limits our ability to secure data privacy or use high-performance distributed/parallel computing platforms. To alleviate such limitations, in this paper, we study the federated training of DeepONets for the first time. That is, we develop a framework, which we refer to as Fed-DeepONet, that allows multiple clients to train DeepONets collaboratively under the coordination of a centralized server. To achieve Fed-DeepONets, we propose an efficient stochastic gradient-based algorithm that enables the distributed optimization of the DeepONet parameters by averaging first-order estimates of the DeepONet loss gradient. Then, to accelerate the training convergence of Fed-DeepONets, we propose a moment-enhanced (i.e., adaptive) stochastic gradient-based strategy. Finally, we verify the performance of Fed-DeepONet by learning, for different configurations of the number of clients and fractions of available clients, (i) the solution operator of a gravity pendulum and (ii) the dynamic response of a parametric library of pendulums.
Audience	Academic
Author	Moya, Christian Lin, Guang
Author_xml	– sequence: 1 givenname: Christian surname: Moya fullname: Moya, Christian – sequence: 2 givenname: Guang orcidid: 0000-0002-0976-1987 surname: Lin fullname: Lin, Guang
BackLink	https://www.osti.gov/biblio/1886960$$D View this record in Osti.gov
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Cites_doi	10.1109/JPROC.2020.2998530 10.1137/20M1342859 10.1109/72.392253 10.1073/pnas.1517384113 10.1016/j.ifacol.2016.10.249 10.1016/j.jcp.2021.110296 10.1016/j.neucom.2023.03.015 10.1038/nature14539 10.1016/j.jcp.2018.10.045 10.1016/j.jcp.2019.06.042 10.1038/s42256-021-00302-5
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References	Schaeffer (ref_8) 2017; 473 Lu (ref_10) 2021; 3 Qin (ref_2) 2019; 395 ref_14 Raissi (ref_5) 2019; 378 ref_12 LeCun (ref_1) 2015; 521 ref_19 ref_18 ref_16 ref_15 Li (ref_17) 2020; 37 Chen (ref_11) 1995; 6 Cai (ref_13) 2021; 436 Qin (ref_3) 2021; 43 Minerva (ref_9) 2020; 108 ref_25 ref_24 ref_23 ref_22 ref_21 ref_20 ref_27 ref_26 Brunton (ref_6) 2016; 113 Brunton (ref_7) 2016; 49 ref_4
References_xml	– volume: 473 start-page: 20160446 year: 2017 ident: ref_8 article-title: Learning partial differential equations via data discovery and sparse optimization publication-title: Proc. R. Soc. A Math. Phys. Eng. Sci. – ident: ref_24 – ident: ref_26 – volume: 108 start-page: 1785 year: 2020 ident: ref_9 article-title: Digital twin in the IoT context: A survey on technical features, scenarios, and architectural models publication-title: Proc. IEEE doi: 10.1109/JPROC.2020.2998530 – volume: 43 start-page: A1607 year: 2021 ident: ref_3 article-title: Data-driven learning of nonautonomous systems publication-title: SIAM J. Sci. Comput. doi: 10.1137/20M1342859 – ident: ref_16 – ident: ref_18 – ident: ref_23 – ident: ref_21 – volume: 37 start-page: 50 year: 2020 ident: ref_17 article-title: Federated Learning: Challenges, Methods, and Future Directions publication-title: IEEE Signal Process. Mag. – volume: 6 start-page: 911 year: 1995 ident: ref_11 article-title: Universal approximation to nonlinear operators by neural networks with arbitrary activation functions and its application to dynamical systems publication-title: IEEE Trans. Neural Netw. doi: 10.1109/72.392253 – ident: ref_25 – ident: ref_4 – volume: 113 start-page: 3932 year: 2016 ident: ref_6 article-title: Discovering governing equations from data by sparse identification of nonlinear dynamical systems publication-title: Proc. Natl. Acad. Sci. USA doi: 10.1073/pnas.1517384113 – ident: ref_27 – volume: 49 start-page: 710 year: 2016 ident: ref_7 article-title: Sparse identification of nonlinear dynamics with control (SINDYc) publication-title: IFAC-PapersOnLine doi: 10.1016/j.ifacol.2016.10.249 – volume: 436 start-page: 110296 year: 2021 ident: ref_13 article-title: DeepM&Mnet: Inferring the electroconvection multiphysics fields based on operator approximation by neural networks publication-title: J. Comput. Phys. doi: 10.1016/j.jcp.2021.110296 – ident: ref_12 – ident: ref_14 doi: 10.1016/j.neucom.2023.03.015 – volume: 521 start-page: 436 year: 2015 ident: ref_1 article-title: Deep learning publication-title: Nature doi: 10.1038/nature14539 – ident: ref_15 – volume: 378 start-page: 686 year: 2019 ident: ref_5 article-title: Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations publication-title: J. Comput. Phys. doi: 10.1016/j.jcp.2018.10.045 – volume: 395 start-page: 620 year: 2019 ident: ref_2 article-title: Data driven governing equations approximation using deep neural networks publication-title: J. Comput. Phys. doi: 10.1016/j.jcp.2019.06.042 – volume: 3 start-page: 218 year: 2021 ident: ref_10 article-title: Learning nonlinear operators via DeepONet based on the universal approximation theorem of operators publication-title: Nat. Mach. Intell. doi: 10.1038/s42256-021-00302-5 – ident: ref_19 – ident: ref_22 – ident: ref_20
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SubjectTerms	Algorithms Analysis Clients Communication Computational linguistics Computer architecture Data security deep learning deep operator networks Digital twins Dynamic response Dynamical systems Engineering Experiments federated learning Language processing Natural language interfaces Neural networks Optimization Pendulums Privacy stochastic-gradient descent Training
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Title	Fed-DeepONet: Stochastic Gradient-Based Federated Training of Deep Operator Networks
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