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Jul, 2023
利用物理知识驱动的神经网络解决维度灾难
Tackling the Curse of Dimensionality with Physics-Informed Neural Networks
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Zheyuan Hu, Khemraj Shukla, George Em Karniadakis, Kenji Kawaguchi
TL;DR
开发了一种名为Stochastic Dimension Gradient Descent (SDGD)的新方法,用于扩展物理信息神经网络(PINNs)以解决任意高维PDEs,并理论上证明了其收敛性和其他所需属性。
Abstract
The
curse-of-dimensionality
(CoD) taxes computational resources heavily with exponentially increasing computational cost as the dimension increases. This poses great challenges in solving
high-dimensional pdes
as
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