Zobrazeno 1 - 10
of 141
pro vyhledávání: '"Lu, Yulong"'
Autor:
Lu, Yulong, Xu, Wuzhe
Solving partial differential equations (PDEs) on fine spatio-temporal scales for high-fidelity solutions is critical for numerous scientific breakthroughs. Yet, this process can be prohibitively expensive, owing to the inherent complexities of the pr
Externí odkaz:
http://arxiv.org/abs/2404.05009
For the ground state of the Gross-Pitaevskii (GP) eigenvalue problem, we consider a fully discretized Sobolev gradient flow, which can be regarded as the Riemannian gradient descent on the sphere under a metric induced by a modified $H^1$-norm. We pr
Externí odkaz:
http://arxiv.org/abs/2403.06028
Autor:
Cole, Frank, Lu, Yulong
While score-based generative models (SGMs) have achieved remarkable success in enormous image generation tasks, their mathematical foundations are still limited. In this paper, we analyze the approximation and generalization of SGMs in learning a fam
Externí odkaz:
http://arxiv.org/abs/2402.08082
Autor:
Yang, Yahong, Lu, Yulong
This paper establishes the nearly optimal rate of approximation for deep neural networks (DNNs) when applied to Korobov functions, effectively overcoming the curse of dimensionality. The approximation results presented in this paper are measured with
Externí odkaz:
http://arxiv.org/abs/2311.04779
We study the convergences of three projected Sobolev gradient flows to the ground state of the Gross-Pitaevskii eigenvalue problem. They are constructed as the gradient flows of the Gross-Pitaevskii energy functional with respect to the $H^1_0$-metri
Externí odkaz:
http://arxiv.org/abs/2301.09818
Autor:
Lu, Yulong
Finding the mixed Nash equilibria (MNE) of a two-player zero sum continuous game is an important and challenging problem in machine learning. A canonical algorithm to finding the MNE is the noisy gradient descent ascent method which in the infinite p
Externí odkaz:
http://arxiv.org/abs/2212.08791
Deep operator network (DeepONet) has demonstrated great success in various learning tasks, including learning solution operators of partial differential equations. In particular, it provides an efficient approach to predict the evolution equations in
Externí odkaz:
http://arxiv.org/abs/2212.04663
Publikováno v:
Nonlinearity 36.11 (2023): 5731
Motivated by the challenge of sampling Gibbs measures with nonconvex potentials, we study a continuum birth-death dynamics. We improve results in previous works [51,57] and provide weaker hypotheses under which the probability density of the birth-de
Externí odkaz:
http://arxiv.org/abs/2211.00450
Spectral Barron spaces have received considerable interest recently as it is the natural function space for approximation theory of two-layer neural networks with a dimension-free convergence rate. In this paper we study the regularity of solutions t
Externí odkaz:
http://arxiv.org/abs/2201.10072
Autor:
Wang, Peng, Mao, Jingwen, Ye, Huishou, Wang, Yitian, Jian, Wei, Song, Shiwei, Yan, Jianming, Wan, Limin, Lu, Yulong, Ren, Bozhi
Publikováno v:
In Ore Geology Reviews June 2024 169