Mathematics > Dynamical Systems
arXiv:2401.03728 (math)
[Submitted on 8 Jan 2024 (v1), last revised 9 Jan 2024 (this version, v2)]
Title:Generalized Lagrangian Neural Networks
View a PDF of the paper titled Generalized Lagrangian Neural Networks, by Shanshan Xiao and 2 other authors
View PDFHTML (experimental)Abstract:Incorporating neural networks for the solution of Ordinary Differential Equations (ODEs) represents a pivotal research direction within computational mathematics. Within neural network architectures, the integration of the intrinsic structure of ODEs offers advantages such as enhanced predictive capabilities and reduced data utilization. Among these structural ODE forms, the Lagrangian representation stands out due to its significant physical underpinnings. Building upon this framework, Bhattoo introduced the concept of Lagrangian Neural Networks (LNNs). Then in this article, we introduce a groundbreaking extension (Genralized Lagrangian Neural Networks) to Lagrangian Neural Networks (LNNs), innovatively tailoring them for non-conservative systems. By leveraging the foundational importance of the Lagrangian within Lagrange's equations, we formulate the model based on the generalized Lagrange's equation. This modification not only enhances prediction accuracy but also guarantees Lagrangian representation in non-conservative systems. Furthermore, we perform various experiments, encompassing 1-dimensional and 2-dimensional examples, along with an examination of the impact of network parameters, which proved the superiority of Generalized Lagrangian Neural Networks(GLNNs).
| Subjects: | Dynamical Systems (math.DS); Machine Learning (cs.LG); Numerical Analysis (math.NA) |
| Cite as: | arXiv:2401.03728 [math.DS] |
| (orarXiv:2401.03728v2 [math.DS] for this version) | |
| https://doi.org/10.48550/arXiv.2401.03728 arXiv-issued DOI via DataCite |
Submission history
From: Shanshan Xiao [view email][v1] Mon, 8 Jan 2024 08:26:40 UTC (1,838 KB)
[v2] Tue, 9 Jan 2024 11:24:16 UTC (492 KB)
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View a PDF of the paper titled Generalized Lagrangian Neural Networks, by Shanshan Xiao and 2 other authors
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