Zobrazeno 1 - 10
of 149
pro vyhledávání: '"Lu, Yulong"'
This paper is concerned with effective approximations and wall laws of viscous laminar flows in 3D pipes with randomly rough boundaries. The random roughness is characterized by the boundary oscillation scale $\varepsilon \ll 1 $ and a probability sp
Externí odkaz:
http://arxiv.org/abs/2411.11653
Foundation models for natural language processing, powered by the transformer architecture, exhibit remarkable in-context learning (ICL) capabilities, allowing pre-trained models to adapt to downstream tasks using few-shot prompts without updating th
Externí odkaz:
http://arxiv.org/abs/2409.12293
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
This paper studies the numerical approximation of the ground state of the Gross-Pitaevskii (GP) eigenvalue problem with a fully discretized Sobolev gradient flow induced by the $H^1$ norm. For the spatial discretization, we consider the finite elemen
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