Zobrazeno 1 - 10
of 375
pro vyhledávání: '"Zhao, Hongkai"'
A mean-field game (MFG) seeks the Nash Equilibrium of a game involving a continuum of players, where the Nash Equilibrium corresponds to a fixed point of the best-response mapping. However, simple fixed-point iterations do not always guarantee conver
Externí odkaz:
http://arxiv.org/abs/2411.07989
In this work, we propose a balanced multi-component and multi-layer neural network (MMNN) structure to approximate functions with complex features with both accuracy and efficiency in terms of degrees of freedom and computation cost. The main idea is
Externí odkaz:
http://arxiv.org/abs/2407.00765
Publikováno v:
Journal of Machine Learning Research, 25(35):1--39, 2024
This paper explores the expressive power of deep neural networks for a diverse range of activation functions. An activation function set $\mathscr{A}$ is defined to encompass the majority of commonly used activation functions, such as $\mathtt{ReLU}$
Externí odkaz:
http://arxiv.org/abs/2307.06555
In this work, a comprehensive numerical study involving analysis and experiments shows why a two-layer neural network has difficulties handling high frequencies in approximation and learning when machine precision and computation cost are important f
Externí odkaz:
http://arxiv.org/abs/2306.17301
Publikováno v:
Proceedings of the 40th International Conference on Machine Learning, PMLR 202:41452-41487, 2023
This paper explores the expressive power of deep neural networks through the framework of function compositions. We demonstrate that the repeated compositions of a single fixed-size ReLU network exhibit surprising expressive power, despite the limite
Externí odkaz:
http://arxiv.org/abs/2301.12353
Publikováno v:
Foundations of Computational Mathematics. Oct2024, Vol. 24 Issue 5, p1595-1641. 47p.
Autor:
Zhao, Hongkai1,2 (AUTHOR) zhaohongkai@zju.edu.cn, Zhou, Yudi1 (AUTHOR) zhouyudi@zju.edu.cn, Gu, Qiuling1 (AUTHOR) guqiuling@zju.edu.cn, Han, Yicai3 (AUTHOR) hanyicai@163.com, Wu, Hongda1 (AUTHOR) hongdawu94@zju.edu.cn, Xu, Peituo1 (AUTHOR) xupeituo@zju.edu.cn, Lin, Lei1 (AUTHOR) linlei@zju.edu.cn, Lv, Weige1 (AUTHOR) lvweige@zju.edu.cn, Wu, Lan1 (AUTHOR) wul@zju.edu.cn, Wu, Lingyun1 (AUTHOR) wlyun@zju.edu.cn, Jiang, Chengchong1 (AUTHOR) jiangchengchong@zju.edu.cn, Chen, Yang1 (AUTHOR) chenyang0914@zju.edu.cn, Yuan, Mingzhu1 (AUTHOR) mingzhu@zju.edu.cn, Sun, Wenbo4 (AUTHOR) haitianyise@donghailab.com, Liu, Chong1 (AUTHOR) chongliu@zju.edu.cn, Liu, Dong1,2 (AUTHOR) liudongopt@zju.edu.cn
Publikováno v:
Remote Sensing. Oct2024, Vol. 16 Issue 19, p3579. 17p.
Autor:
Zhao, Hongkai, Zhong, Yimin
Linear evolution PDE $\partial_t u(x,t) = -\mathcal{L} u$, where $\mathcal{L}$ is a strongly elliptic operator independent of time, is studied as an example to show if one can superpose snapshots of a single (or a finite number of) solution(s) to con
Externí odkaz:
http://arxiv.org/abs/2206.05336
In this work we study the problem about learning a partial differential equation (PDE) from its solution data. PDEs of various types are used as examples to illustrate how much the solution data can reveal the PDE operator depending on the underlying
Externí odkaz:
http://arxiv.org/abs/2204.04602
Autor:
Qi, Haina, Jing, Xuelian, Hu, Yaolin, Wu, Ping, Zhang, Xuejian, Li, Yongtao, Zhao, Hongkai, Ma, Qianli, Dong, Xiangting, Mahadevan, C.K.
Publikováno v:
In Composites Part B 1 January 2025 288