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20232025
most citedHutchinson Trace Estimation for High-Dimensional and High-Order Physics-Informed Neural Networks

37 citations · 75 across the 11 of their papers we have counts for

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math.NA2024★ 20 cited

Tackling the Curse of Dimensionality in Fractional and Tempered Fractional PDEs with Physics-Informed Neural Networks

Zheyuan Hu, Kenji Kawaguchi, Zhongqiang Zhang +1

Fractional and tempered fractional partial differential equations (PDEs) are effective models of long-range interactions, anomalous diffusion, and non-local effects. Traditional nu…

math.NA2024

Tensor neural networks for high-dimensional Fokker-Planck equations

Taorui Wang, Zheyuan Hu, Kenji Kawaguchi +2

We solve high-dimensional steady-state Fokker-Planck equations on the whole space by applying tensor neural networks. The tensor networks are a linear combination of tensor product…