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cs.LG2026
fTNN: a tensor neural network for fractional PDEs
Qingkui Ma, Hehu Xie, Xiaobo Yin
We develop the fTNN, a deterministic tensor neural network subspace method for problems involving the fractional Laplacian on bounded domains, taking the fractional Poisson equatio…
math.NA2026
Quadrature-Enhanced Monte Carlo fPINN Method for High-Dimensional Fractional PDEs
Qingkui Ma, Hehu Xie, Xiaobo Yin
Fractional PDEs involving the fractional Laplacian on bounded domains are challenging because of hypersingular nonlocal kernels, exterior Dirichlet constraints, reduced boundary re…
math.NA2026
Analysis of Convergence for the IPA-AC Method
Xiuzhu Yang, Xiaobo Yin
The Improved Partial Area-Analytical Calculation (IPA-AC) method represents a leading meshfree discretization strategy for peridynamic models, distinguished by its rigorous geometr…