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D3M: A Deep Domain Decomposition Method for Partial Differential Equations
- Source :
- IEEE Access, Vol 8, Pp 5283-5294 (2020)
- Publication Year :
- 2020
- Publisher :
- Institute of Electrical and Electronics Engineers (IEEE), 2020.
-
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 multi-fidelity neural network framework to solve this optimization problem. Our contribution is to develop a systematical computational procedure for the underlying problem in parallel with domain decomposition. Our analysis shows that the D3M approximation solution converges to the exact solution of underlying PDEs. Our proposed framework establishes a foundation to use variational deep learning in large-scale engineering problems and designs. We present a general mathematical framework of D3M, validate its accuracy and demonstrate its efficiency with numerical experiments.
- Subjects :
- FOS: Computer and information sciences
Computer Science - Machine Learning
Optimization problem
General Computer Science
Computer science
010103 numerical & computational mathematics
01 natural sciences
Machine Learning (cs.LG)
Variational principle
FOS: Mathematics
Applied mathematics
General Materials Science
Mathematics - Numerical Analysis
Domain decomposition
0101 mathematics
mesh-free
Partial differential equation
Artificial neural network
business.industry
Deep learning
General Engineering
deep learning
Domain decomposition methods
Numerical Analysis (math.NA)
010101 applied mathematics
Exact solutions in general relativity
physics-constrained
lcsh:Electrical engineering. Electronics. Nuclear engineering
Artificial intelligence
parallel computation
PDEs
business
lcsh:TK1-9971
Subjects
Details
- ISSN :
- 21693536
- Volume :
- 8
- Database :
- OpenAIRE
- Journal :
- IEEE Access
- Accession number :
- edsair.doi.dedup.....a0e2143ea75533ab030926343958ffaf