D3M: A Deep Domain Decomposition Method for Partial Differential Equations

A state-of-the-art deep domain decomposition method (D3M) based on the variational principle is proposed for partial differential equations (PDEs). The solution of PDEs can be formulated as the solution of a constrained optimization problem, and we design a hierarchical neural network framework to s...
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Autor*in:	Ke Li [verfasserIn] Kejun Tang [verfasserIn] Tianfan Wu [verfasserIn] Qifeng Liao [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2020

Schlagwörter:	Domain decomposition deep learning mesh-free parallel computation PDEs physics-constrained

Übergeordnetes Werk:	In: IEEE Access - IEEE, 2014, 8(2020), Seite 5283-5294
Übergeordnetes Werk:	volume:8 ; year:2020 ; pages:5283-5294

Links:	Link aufrufen Link aufrufen Link aufrufen Journal toc

DOI / URN:	10.1109/ACCESS.2019.2957200

Katalog-ID:	DOAJ057738327

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spelling	10.1109/ACCESS.2019.2957200 doi (DE-627)DOAJ057738327 (DE-599)DOAJ1c4809619fd74d03a61924a30899a025 DE-627 ger DE-627 rakwb eng TK1-9971 Ke Li verfasserin aut D3M: A Deep Domain Decomposition Method for Partial Differential Equations 2020 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier A state-of-the-art deep domain decomposition method (D3M) based on the variational principle is proposed for partial differential equations (PDEs). The solution of PDEs can be formulated as the solution of a constrained optimization problem, and we design a hierarchical neural network framework to solve this optimization problem. Through decomposing a PDE system into components parts, our D3M builds local neural networks on physical subdomains independently (which can be implemented in parallel), so as to obtain efficient neural network approximations for complex problems. Our analysis shows that the D3M approximation solution converges to the exact solution of the underlying PDEs. The accuracy and the efficiency of D3M are validated and demonstrated with numerical experiments. Domain decomposition deep learning mesh-free parallel computation PDEs physics-constrained Electrical engineering. Electronics. Nuclear engineering Kejun Tang verfasserin aut Tianfan Wu verfasserin aut Qifeng Liao verfasserin aut In IEEE Access IEEE, 2014 8(2020), Seite 5283-5294 (DE-627)728440385 (DE-600)2687964-5 21693536 nnns volume:8 year:2020 pages:5283-5294 https://doi.org/10.1109/ACCESS.2019.2957200 kostenfrei https://doaj.org/article/1c4809619fd74d03a61924a30899a025 kostenfrei https://ieeexplore.ieee.org/document/8918421/ kostenfrei https://doaj.org/toc/2169-3536 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2014 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 8 2020 5283-5294
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allfieldsSound	10.1109/ACCESS.2019.2957200 doi (DE-627)DOAJ057738327 (DE-599)DOAJ1c4809619fd74d03a61924a30899a025 DE-627 ger DE-627 rakwb eng TK1-9971 Ke Li verfasserin aut D3M: A Deep Domain Decomposition Method for Partial Differential Equations 2020 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier A state-of-the-art deep domain decomposition method (D3M) based on the variational principle is proposed for partial differential equations (PDEs). The solution of PDEs can be formulated as the solution of a constrained optimization problem, and we design a hierarchical neural network framework to solve this optimization problem. Through decomposing a PDE system into components parts, our D3M builds local neural networks on physical subdomains independently (which can be implemented in parallel), so as to obtain efficient neural network approximations for complex problems. Our analysis shows that the D3M approximation solution converges to the exact solution of the underlying PDEs. The accuracy and the efficiency of D3M are validated and demonstrated with numerical experiments. Domain decomposition deep learning mesh-free parallel computation PDEs physics-constrained Electrical engineering. Electronics. Nuclear engineering Kejun Tang verfasserin aut Tianfan Wu verfasserin aut Qifeng Liao verfasserin aut In IEEE Access IEEE, 2014 8(2020), Seite 5283-5294 (DE-627)728440385 (DE-600)2687964-5 21693536 nnns volume:8 year:2020 pages:5283-5294 https://doi.org/10.1109/ACCESS.2019.2957200 kostenfrei https://doaj.org/article/1c4809619fd74d03a61924a30899a025 kostenfrei https://ieeexplore.ieee.org/document/8918421/ kostenfrei https://doaj.org/toc/2169-3536 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2014 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 8 2020 5283-5294
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callnumber-first	T - Technology
author	Ke Li
spellingShingle	Ke Li misc TK1-9971 misc Domain decomposition misc deep learning misc mesh-free misc parallel computation misc PDEs misc physics-constrained misc Electrical engineering. Electronics. Nuclear engineering D3M: A Deep Domain Decomposition Method for Partial Differential Equations
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topic_title	TK1-9971 D3M: A Deep Domain Decomposition Method for Partial Differential Equations Domain decomposition deep learning mesh-free parallel computation PDEs physics-constrained
topic	misc TK1-9971 misc Domain decomposition misc deep learning misc mesh-free misc parallel computation misc PDEs misc physics-constrained misc Electrical engineering. Electronics. Nuclear engineering
topic_unstemmed	misc TK1-9971 misc Domain decomposition misc deep learning misc mesh-free misc parallel computation misc PDEs misc physics-constrained misc Electrical engineering. Electronics. Nuclear engineering
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title	D3M: A Deep Domain Decomposition Method for Partial Differential Equations
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title_sort	d3m: a deep domain decomposition method for partial differential equations
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title_auth	D3M: A Deep Domain Decomposition Method for Partial Differential Equations
abstract	A state-of-the-art deep domain decomposition method (D3M) based on the variational principle is proposed for partial differential equations (PDEs). The solution of PDEs can be formulated as the solution of a constrained optimization problem, and we design a hierarchical neural network framework to solve this optimization problem. Through decomposing a PDE system into components parts, our D3M builds local neural networks on physical subdomains independently (which can be implemented in parallel), so as to obtain efficient neural network approximations for complex problems. Our analysis shows that the D3M approximation solution converges to the exact solution of the underlying PDEs. The accuracy and the efficiency of D3M are validated and demonstrated with numerical experiments.
abstractGer	A state-of-the-art deep domain decomposition method (D3M) based on the variational principle is proposed for partial differential equations (PDEs). The solution of PDEs can be formulated as the solution of a constrained optimization problem, and we design a hierarchical neural network framework to solve this optimization problem. Through decomposing a PDE system into components parts, our D3M builds local neural networks on physical subdomains independently (which can be implemented in parallel), so as to obtain efficient neural network approximations for complex problems. Our analysis shows that the D3M approximation solution converges to the exact solution of the underlying PDEs. The accuracy and the efficiency of D3M are validated and demonstrated with numerical experiments.
abstract_unstemmed	A state-of-the-art deep domain decomposition method (D3M) based on the variational principle is proposed for partial differential equations (PDEs). The solution of PDEs can be formulated as the solution of a constrained optimization problem, and we design a hierarchical neural network framework to solve this optimization problem. Through decomposing a PDE system into components parts, our D3M builds local neural networks on physical subdomains independently (which can be implemented in parallel), so as to obtain efficient neural network approximations for complex problems. Our analysis shows that the D3M approximation solution converges to the exact solution of the underlying PDEs. The accuracy and the efficiency of D3M are validated and demonstrated with numerical experiments.
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title_short	D3M: A Deep Domain Decomposition Method for Partial Differential Equations
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