Deep Learning Nonhomogeneous Elliptic Interface Problems by Soft Constraint Physics-Informed Neural Networks Article Swipe
Fujun Cao
,
Xiaobin Guo
,
Fei Gao
,
Dongfang Yuan
·
YOU?
·
· 2023
· Open Access
·
· DOI: https://doi.org/10.3390/math11081843
YOU?
·
· 2023
· Open Access
·
· DOI: https://doi.org/10.3390/math11081843
It is a great challenge to solve nonhomogeneous elliptic interface problems, because the interface divides the computational domain into two disjoint parts, and the solution may change dramatically across the interface. A soft constraint physics-informed neural network with dual neural networks is proposed, which is composed of two separate neural networks for each subdomain, which are coupled by the connecting conditions on the interface. It is beneficial to capture the singularity of the solution across the interface. We formulate the PDEs, boundary conditions, and jump conditions on the interface into the loss function by means of the physics-informed neural network (PINN), and the different terms in the loss function are balanced by optimized penalty weights. To enhance computing efficiency for increasingly difficult issues, adaptive activation functions and the adaptive sampled method are used, which may be improved to produce the optimal network performance, as the topology of the loss function involved in the optimization process changes dynamically. Lastly, we present many numerical experiments, in both 2D and 3D, to demonstrate the proposed method’s flexibility, efficacy, and accuracy in tackling nonhomogeneous interface issues.
Related Topics
Concepts
Interface (matter)
Artificial neural network
Constraint (computer-aided design)
Computer science
Boundary (topology)
Disjoint sets
Function (biology)
Flexibility (engineering)
Singularity
Topology (electrical circuits)
Mathematical optimization
Mathematics
Artificial intelligence
Geometry
Mathematical analysis
Parallel computing
Evolutionary biology
Maximum bubble pressure method
Combinatorics
Bubble
Biology
Statistics
Metadata
- Type
- article
- Language
- en
- Landing Page
- https://doi.org/10.3390/math11081843
- https://www.mdpi.com/2227-7390/11/8/1843/pdf?version=1681362072
- OA Status
- gold
- Cited By
- 5
- References
- 45
- Related Works
- 10
- OpenAlex ID
- https://openalex.org/W4365453697
All OpenAlex metadata
Raw OpenAlex JSON
- OpenAlex ID
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https://openalex.org/W4365453697Canonical identifier for this work in OpenAlex
- DOI
-
https://doi.org/10.3390/math11081843Digital Object Identifier
- Title
-
Deep Learning Nonhomogeneous Elliptic Interface Problems by Soft Constraint Physics-Informed Neural NetworksWork title
- Type
-
articleOpenAlex work type
- Language
-
enPrimary language
- Publication year
-
2023Year of publication
- Publication date
-
2023-04-13Full publication date if available
- Authors
-
Fujun Cao, Xiaobin Guo, Fei Gao, Dongfang YuanList of authors in order
- Landing page
-
https://doi.org/10.3390/math11081843Publisher landing page
- PDF URL
-
https://www.mdpi.com/2227-7390/11/8/1843/pdf?version=1681362072Direct link to full text PDF
- Open access
-
YesWhether a free full text is available
- OA status
-
goldOpen access status per OpenAlex
- OA URL
-
https://www.mdpi.com/2227-7390/11/8/1843/pdf?version=1681362072Direct OA link when available
- Concepts
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Interface (matter), Artificial neural network, Constraint (computer-aided design), Computer science, Boundary (topology), Disjoint sets, Function (biology), Flexibility (engineering), Singularity, Topology (electrical circuits), Mathematical optimization, Mathematics, Artificial intelligence, Geometry, Mathematical analysis, Parallel computing, Evolutionary biology, Maximum bubble pressure method, Combinatorics, Bubble, Biology, StatisticsTop concepts (fields/topics) attached by OpenAlex
- Cited by
-
5Total citation count in OpenAlex
- Citations by year (recent)
-
2025: 2, 2024: 2, 2023: 1Per-year citation counts (last 5 years)
- References (count)
-
45Number of works referenced by this work
- Related works (count)
-
10Other works algorithmically related by OpenAlex
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