English(EN) Deep neural networks with ReLU, leaky ReLU, and softplus activation provably overcome the curse of dimensionality for Kolmogorov partial differential equations with Lipschitz nonlinearities in the $L^p$-sense

深度神经网络可证明地克服了偏微分方程的维度灾难

作者 PulseAugur 编辑部 · [1 个来源] · 2026-04-30 04:00

研究人员证明了深度神经网络（DNN）在逼近Kolmogorov偏微分方程解时可以克服维度灾难。这项数学证明扩展了先前的发现，表明使用ReLU、Leaky ReLU和Softplus激活函数的网络可以在不导致计算成本相对于问题维度呈指数级增长的情况下，实现逼近精度。该工作在$L^p$意义下，针对广泛的$p$值证明了这种能力。 AI

影响为使用深度学习解决高维科学计算问题提供了理论基础。

排序理由学术论文，提出了深度神经网络克服计算挑战的理论证明。

在 arXiv cs.LG 阅读 →

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报道来源 [1]

arXiv cs.LG TIER_1 English(EN) · Julia Ackermann, Arnulf Jentzen, Thomas Kruse, Benno Kuckuck, Joshua Lee Padgett · 2026-04-30 04:00

具有 ReLU、leaky ReLU 和 softplus 激活的深度神经网络可证明地克服了 $L^p$ 意义下具有 Lipschitz 非线性的 Kolmogorov 偏微分方程的维度灾难

arXiv:2309.13722v3 Announce Type: replace-cross Abstract: Recently, several deep learning (DL) methods for approximating high-dimensional partial differential equations (PDEs) have been proposed. The interest that these methods have generated in the literature is in large part du…

本文如何被排名

报道来源 [1]

具有 ReLU、leaky ReLU 和 softplus 激活的深度神经网络可证明地克服了 $L^p$ 意义下具有 Lipschitz 非线性的 Kolmogorov 偏微分方程的维度灾难

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