Solving The Initial Value Problem Of Ordinary Differential Equations ...

Mathematics > Numerical Analysis arXiv:2203.03479 (math) [Submitted on 7 Mar 2022] Title:Solving the Initial Value Problem of Ordinary Differential Equations by Lie Group based Neural Network Method Authors:Ying Wen, Temuer Chaolu, Xiangsheng Wang View a PDF of the paper titled Solving the Initial Value Problem of Ordinary Differential Equations by Lie Group based Neural Network Method, by Ying Wen and 2 other authors View PDF

Abstract:To combine a feedforward neural network (FNN) and Lie group (symmetry) theory of differential equations (DEs), an alternative artificial NN approach is proposed to solve the initial value problems (IVPs) of ordinary DEs (ODEs). Introducing the Lie group expressions of the solution, the trial solution of ODEs is split into two parts. The first part is a solution of other ODEs with initial values of original IVP. This is easily solved using the Lie group and known symbolic or numerical methods without any network parameters (weights and biases). The second part consists of an FNN with adjustable parameters. This is trained using the error back propagation method by minimizing an error (loss) function and updating the parameters. The method significantly reduces the number of the trainable parameters and can more quickly and accurately learn the real solution, compared to the existing similar methods. The numerical method is applied to several cases, including physical oscillation problems. The results have been graphically represented, and some conclusions have been made.

Subjects:	Numerical Analysis (math.NA)
Cite as:	arXiv:2203.03479 [math.NA]
(or arXiv:2203.03479v1 [math.NA] for this version)
https://doi.org/10.48550/arXiv.2203.03479 Focus to learn more arXiv-issued DOI via DataCite
Related DOI:	https://doi.org/10.1371/journal.pone.0265992 Focus to learn more DOI(s) linking to related resources

Submission history

From: Ying Wen [view email] [v1] Mon, 7 Mar 2022 15:49:05 UTC (193 KB) Full-text links:

Access Paper:

View a PDF of the paper titled Solving the Initial Value Problem of Ordinary Differential Equations by Lie Group based Neural Network Method, by Ying Wen and 2 other authors
• View PDF
• TeX Source

view license Current browse context: math.NA < prev | next > new | recent | 2022-03 Change to browse by: cs cs.NA math

References & Citations

• NASA ADS
• Google Scholar
• Semantic Scholar

export BibTeX citation

BibTeX formatted citation

× loading... Data provided by:

Bookmark

Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv (What is alphaXiv?) Links to Code Toggle CatalyzeX Code Finder for Papers (What is CatalyzeX?) DagsHub Toggle DagsHub (What is DagsHub?) GotitPub Toggle Gotit.pub (What is GotitPub?) Huggingface Toggle Hugging Face (What is Huggingface?) Links to Code Toggle Papers with Code (What is Papers with Code?) ScienceCast Toggle ScienceCast (What is ScienceCast?) Demos Demos Replicate Toggle Replicate (What is Replicate?) Spaces Toggle Hugging Face Spaces (What is Spaces?) Spaces Toggle TXYZ.AI (What is TXYZ.AI?) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower (What are Influence Flowers?) Core recommender toggle CORE Recommender (What is CORE?)

• Author
• Venue
• Institution
• Topic

About arXivLabs arXivLabs: experimental projects with community collaborators

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.

Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)