English(EN) fTNN: a tensor neural network for fractional PDEs

新型张量神经网络以高精度解决分数阶偏微分方程

作者 PulseAugur 编辑部 · [3 个来源] · 2026-06-25 15:13

研究人员开发了fTNN，这是一种确定性张量神经网络，用于求解分数阶偏微分方程（PDE）。该方法采用几何自适应积分分裂和专门的求积技术来处理分数阶拉普拉斯算子。该框架对于具有强边界奇异性和长时间模拟的问题特别有效，与现有的fPINN和蒙特卡洛基线相比，精度有所提高。 AI

影响引入了一种新颖的神经网络架构来解决复杂的数学问题，可能推动科学计算的发展。

排序理由该集群描述了一篇关于使用张量神经网络解决分数阶偏微分方程的新颖方法的最新研究论文。

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arXiv cs.LG TIER_1 English(EN) · Qingkui Ma, Hehu Xie, Xiaobo Yin · 2026-06-26 04:00

fTNN：用于分数阶偏微分方程的张量神经网络

arXiv:2606.27140v1 Announce Type: new Abstract: We develop the fTNN, a deterministic tensor neural network subspace method for problems involving the fractional Laplacian on bounded domains, taking the fractional Poisson equation and time-dependent fractional advection-diffusion …
arXiv cs.LG TIER_1 English(EN) · Xiaobo Yin · 2026-06-25 15:13

fTNN：一种用于分数阶偏微分方程的张量神经网络

We develop the fTNN, a deterministic tensor neural network subspace method for problems involving the fractional Laplacian on bounded domains, taking the fractional Poisson equation and time-dependent fractional advection-diffusion equation as typical representatives. The work em…
Hugging Face Daily Papers TIER_1 English(EN) · 2026-06-25 15:13

fTNN：用于分数阶偏微分方程的张量神经网络

We develop the fTNN, a deterministic tensor neural network subspace method for problems involving the fractional Laplacian on bounded domains, taking the fractional Poisson equation and time-dependent fractional advection-diffusion equation as typical representatives. The work em…