English(EN) Simultaneous CNN Approximation on Manifolds with Applications to Boundary Value Problems

流形上的CNN在边界值问题中提高了精度

作者 PulseAugur 编辑部 · [1 个来源] · 2026-05-07 04:00

研究人员开发了新颖的卷积神经网络（CNN）方法，用于在紧致黎曼流形上近似函数和求解椭圆边值问题。这些方法展示了比标准方法更高的近似率，该近似率取决于流形的内在维度而非其环境维度，有助于克服维度灾难。提出的物理信息CNN（PICNN）框架通过引入谱边界损失来专门解决边值问题，与标准的物理信息神经网络（PINNs）相比，提高了精度、收敛性和稳定性。 AI

影响引入了用于流形近似和边值问题的新颖CNN技术，有望提高科学计算的精度。

排序理由这是一篇研究论文，详细介绍了在流形上进行CNN近似和求解边值问题的新方法。[lever_c_demoted from research: ic=1 ai=1.0]

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arXiv cs.LG TIER_1 English(EN) · Hanfei Zhou, Lei Shi · 2026-05-07 04:00

Simultaneous CNN Approximation on Manifolds with Applications to Boundary Value Problems

arXiv:2605.04126v1 Announce Type: new Abstract: This paper develops convolutional neural network (CNN) methods for simultaneous approximation and elliptic boundary value problems on compact Riemannian manifolds. We establish simultaneous Sobolev approximation results for single- …

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Simultaneous CNN Approximation on Manifolds with Applications to Boundary Value Problems

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