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TENSOR NEURAL NETWORK--BASED MACHINE LEARNING METHOD FOR ELLIPTIC MULTISCALE PROBLEMS
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AI
DOI：10.1137/24M1648338.png)
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Abstract
En 中文
In this paper, we propose a tensor neural network--based machine learning method for solving elliptic multiscale problems. Leveraging the special structure of tensor neural networks, we can perform direct and highly accurate high-dimensional integration without relying on Monte Carlo methods. Within the framework of the homogenization method, the original multiscale problem is reformulated as several cell problems and a homogenized equation with reasonable accuracy. We then develop a machine learning framework, based on tensor neural networks, to solve the derived equations, especially the high-dimensional cell problems. The proposed method offers a novel approach to designing numerical algorithms for a broader class of multiscale problems with high accuracy. Several numerical examples are presented to demonstrate the effectiveness and accuracy of the proposed method.
Keywords:
elliptic multiscale problem
tensor neural network
high-dimensional integration with high accuracy
homogenization
high-dimensional cell problem
Journal
M
IF:
1.6
Papers:
26
Citations:
0