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Tensor Neural Network Interpolation and Its Applications

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arxiv 2404.07805 v1 pith:IWXBH2UP submitted 2024-04-11 math.NA cs.NA

Yongxin Li , Zhongshuo Lin , Yifan Wang , Hehu Xie This is my paper · ORCID
classification math.NAcs.NA
keywords tensordimensionalhighnetworkneuralinterpolationfunctionsnumerical
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Based on tensor neural network, we propose an interpolation method for high dimensional non-tensor-product-type functions. This interpolation scheme is designed by using the tensor neural network based machine learning method. This means that we use a tensor neural network to approximate high dimensional functions which has no tensor product structure. In some sense, the non-tenor-product-type high dimensional function is transformed to the tensor neural network which has tensor product structure. It is well known that the tensor product structure can bring the possibility to design highly accurate and efficient numerical methods for dealing with high dimensional functions. In this paper, we will concentrate on computing the high dimensional integrations and solving high dimensional partial differential equations. The corresponding numerical methods and numerical examples will be provided to validate the proposed tensor neural network interpolation.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. FieldTNN-based machine learning method for Maxwell eigenvalue problems

    math.NA 2024-11 conditional novelty 6.0 of 10

    A tensor neural network method (FieldTNN) computes Maxwell cavity eigenvalues in tensor and non-tensor domains with a divergence-free penalty that suppresses spurious eigenpairs.

  2. A Kolmogorov High Order Deep Neural Network for High Frequency Partial Differential Equations in High Dimensions

    math.NA 2025-02 conditional novelty 5.0 of 10

    K-HOrderDNN approximates univariate KST components with high-order networks, reducing basis count from (p+1)^d to about d(p+1) and showing strong accuracy on high-frequency, high-dimensional PDE tests.

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