47 citations · 106 across the 22 of their papers we have counts for
10 papers · 1 filter
Near-Optimal Nonconvex Matrix Completion
Jian-Feng Cai, Xiliang Lu, Juntao You
We study nonconvex methods for matrix completion, the problem of recovering a low-rank matrix from a subset of its entries. Convex methods achieve sample complexity linear in the m…
Off-Grid Point-Scatterer Localization from Sparse Limited-Aperture Data via Hankel Completion
Jingzhi Li, Xiliang Lu, Juntao You
We study the localization of distinct planar point scatterers from sparsely sampled single-incidence, single-frequency acoustic far-field data over a limited receiver aperture.…
GraHTP: A Provable Newton-like Algorithm for Sparse Phase Retrieval
Licheng Dai, Xiliang Lu, Juntao You
This paper investigates the sparse phase retrieval problem, which aims to recover a sparse signal from a system of quadratic measurements. In this work, we propose a novel non-conv…
Numerical Recovery of the Diffusion Coefficient in Diffusion Equations from Terminal Measurement
Bangti Jin, Xiliang Lu, Qimeng Quan +1
In this work, we investigate a numerical procedure for recovering a space-dependent diffusion coefficient in a (sub)diffusion model from the given terminal data, and provide a rigo…
On the robustness of double-word addition algorithms
Yuanyuan Yang, XinYu Lyu, Sida He +3
We demonstrate that, even when there are moderate overlaps in the inputs of sloppy or accurate double-word addition algorithms in the QD library, these algorithms still guarantee e…
Current density impedance imaging with PINNs
Chenguang Duan, Yuling Jiao, Xiliang Lu +1
In this paper, we introduce CDII-PINNs, a computationally efficient method for solving CDII using PINNs in the framework of Tikhonov regularization. This method constructs a physic…
Deep Neural Network Approximation of Composition Functions: with application to PINNs
Chenguang Duan, Yuling Jiao, Xiliang Lu +2
In this paper, we focus on approximating a natural class of functions that are compositions of smooth functions. Unlike the low-dimensional support assumption on the covariate, we…
Sample-Efficient Sparse Phase Retrieval via Stochastic Alternating Minimization
Jian-Feng Cai, Yuling Jiao, Xiliang Lu +1
In this work we propose a nonconvex two-stage \underline{s}tochastic \underline{a}lternating \underline{m}inimizing (SAM) method for sparse phase retrieval. The proposed algorithm…
Analysis of Deep Ritz Methods for Laplace Equations with Dirichlet Boundary Conditions
Chenguang Duan, Yuling Jiao, Yanming Lai +3
Deep Ritz methods (DRM) have been proven numerically to be efficient in solving partial differential equations. In this paper, we present a convergence rate in norm for dee…
A rate of convergence of Physics Informed Neural Networks for the linear second order elliptic PDEs
Yuling Jiao, Yanming Lai, Dingwei Li +4
In recent years, physical informed neural networks (PINNs) have been shown to be a powerful tool for solving PDEs empirically. However, numerical analysis of PINNs is still missing…