fTNN is a deterministic tensor neural network subspace method for fractional PDEs that decomposes the fractional Laplacian via spatially dependent integration splits and uses boundary-singularity-aware trial functions to achieve higher accuracy than fPINN and Monte Carlo methods on tested cases.
Tensor neural network interpola- tion and its applications.arXiv preprint arXiv:2404.07805, 2024
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Tensor neural network approximation reduces high-dimensional nonlocal diffusion integrals to low-dimensional ones via separability, with L2 error estimates for Dirichlet and Neumann conditions and tests up to dimension 20.
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fTNN: a tensor neural network for fractional PDEs
fTNN is a deterministic tensor neural network subspace method for fractional PDEs that decomposes the fractional Laplacian via spatially dependent integration splits and uses boundary-singularity-aware trial functions to achieve higher accuracy than fPINN and Monte Carlo methods on tested cases.
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ND-TNN: Tensor-Neural-Network Approximation for High-Dimensional Nonlocal Diffusion Models
Tensor neural network approximation reduces high-dimensional nonlocal diffusion integrals to low-dimensional ones via separability, with L2 error estimates for Dirichlet and Neumann conditions and tests up to dimension 20.