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Tensor Neural Network and Its Numerical Integration

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arxiv 2207.02754 v4 pith:2I3ON7VT submitted 2022-07-06 math.NA cs.NA

Yifan Wang , Pengzhan Jin , Hehu Xie This is my paper · ORCID
classification math.NAcs.NA
keywords numericaltensorintegrationnetworkneuralmethodalgorithmcomplexity
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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.

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Cited by 2 Pith papers

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