Zhao Ding, Yuling Jiao, Xiliang Lu, Peiying Wu, Jerry Zhijian Yang
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引用次数: 0
Abstract
The deep Ritz method (DRM) has recently been shown to be a simple and effective method for solving PDEs. However, the numerical analysis of DRM is still incomplete, especially why over-parameterized DRM works remains unknown. This paper presents the first convergence analysis of the over-parameterized DRM for second-order elliptic equations with Robin boundary conditions. We demonstrate that the convergence rate can be controlled by the weight norm, regardless of the number of parameters in the network. To this end, we establish novel approximation results in Sobolev spaces with norm constraints, which have independent significance.
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Neural Networks is a platform that aims to foster an international community of scholars and practitioners interested in neural networks, deep learning, and other approaches to artificial intelligence and machine learning. Our journal invites submissions covering various aspects of neural networks research, from computational neuroscience and cognitive modeling to mathematical analyses and engineering applications. By providing a forum for interdisciplinary discussions between biology and technology, we aim to encourage the development of biologically-inspired artificial intelligence.
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