English(EN) Residual neural networks overcome the curse of dimensionality for semilinear heat equations

ResNets克服了热方程解的维度灾难

作者 PulseAugur 编辑部 · [1 个来源] · 2026-09-04 04:00

研究人员证明了残差神经网络（ResNets）在逼近半线性热方程解时，能够有效克服维度灾难。该研究提供了理论保证，表明具有参数数量与 $d^{\eta}\varepsilon^{-\eta}$ 成比例的ResNet，可以在维度 $d$ 下实现 $\varepsilon$ 的 $L^2$ 误差逼近解。这项工作将先前关于前馈神经网络的发现扩展到了更复杂的ResNet架构，为高维偏微分方程提供了更有效的数值解法途径。 AI

影响为使用ResNets解决复杂、高维数学问题奠定了理论基础。

排序理由详细介绍神经网络求解微分方程理论结果的学术论文。[lever_c_demoted from research: ic=1 ai=1.0]

在 arXiv cs.LG 阅读 →

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arXiv cs.LG TIER_1 English(EN) · Ilkhom Mukhammadiev, Diyora Salimova · 2026-09-04 04:00

残差神经网络克服了半线性热方程的维度灾难

arXiv:2609.03626v1 Announce Type: cross Abstract: Rigorous results show that feedforward neural networks can overcome the curse of dimensionality in the numerical approximation of high-dimensional partial differential equations (PDEs), but comparatively little is known about resi…

本文如何被排名

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残差神经网络克服了半线性热方程的维度灾难

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