no code implementations • 19 May 2024 • Yuling Jiao, Yanming Lai, Yang Wang
We present error bound in terms of the sample size $n$ and our work provides guidance on how to set the network depth, width, step size, and number of iterations for the projected gradient descent algorithm.
no code implementations • 3 Apr 2024 • Yuling Jiao, Yanming Lai, Yang Wang, Bokai Yan
We present theoretical convergence guarantees for ODE-based generative models, specifically flow matching.
no code implementations • 5 Feb 2023 • Yuling Jiao, Yanming Lai, Yang Wang, Haizhao Yang, Yunfei Yang
This paper analyzes the convergence rate of a deep Galerkin method for the weak solution (DGMW) of second-order elliptic partial differential equations on $\mathbb{R}^d$ with Dirichlet, Neumann, and Robin boundary conditions, respectively.
no code implementations • 28 Feb 2021 • Yuling Jiao, Yanming Lai, Xiliang Lu, Fengru Wang, Jerry Zhijian Yang, Yuanyuan Yang
In this paper, we construct neural networks with ReLU, sine and $2^x$ as activation functions.