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Mathematics > Numerical Analysis

arXiv:2207.02754 (math)
[Submitted on 6 Jul 2022 (v1), last revised 21 Jul 2023 (this version, v4)]

Title:Tensor Neural Network and Its Numerical Integration

Authors:Yifan Wang, Pengzhan Jin, Hehu Xie
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Abstract:In this paper, we introduce a type of tensor neural network. For the first time, we propose its numerical integration scheme and prove the computational complexity to be the polynomial scale of the dimension. Based on the tensor product structure, we develop an efficient numerical integration method by using fixed quadrature points for the functions of the tensor neural network. The corresponding machine learning method is also introduced for solving high-dimensional problems. Some numerical examples are also provided to validate the theoretical results and the numerical algorithm.
Comments: 30 pages, 30 figures
Subjects: Numerical Analysis (math.NA)
MSC classes: 65N30, 65N25, 65L15, 65B99
Cite as: arXiv:2207.02754 [math.NA]
  (or arXiv:2207.02754v4 [math.NA] for this version)
  https://doi.org/10.48550/arXiv.2207.02754

Submission history

From: Hehu Xie [view email]
[v1] Wed, 6 Jul 2022 15:43:04 UTC (138 KB)
[v2] Mon, 31 Oct 2022 16:06:52 UTC (495 KB)
[v3] Tue, 28 Mar 2023 17:24:33 UTC (607 KB)
[v4] Fri, 21 Jul 2023 11:01:41 UTC (934 KB)
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