52 citations · 141 across the 16 of their papers we have counts for
16 papers
Robust Fuzzy local k-plane clustering with mixture distance of hinge loss and L1 norm
Junjun Huang, Xiliang Lu, Xuelin Xie +1
K-plane clustering (KPC), hyperplane clustering, and mixture regression all essentially fall within the same class of problems. This problem can be conceptualized as clustering in…
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…
GAS: A Gaussian Mixture Distribution-Based Adaptive Sampling Method for PINNs
Yuling Jiao, Di Li, Xiliang Lu +2
With the recent study of deep learning in scientific computation, the Physics-Informed Neural Networks (PINNs) method has drawn widespread attention for solving Partial Differentia…
Stability and convergence analysis of high-order numerical schemes with DtN-type absorbing boundary conditions for nonlocal wave equations
Jihong Wang, Jerry Zhijian Yang, Jiwei Zhang
The stability and convergence analysis of high-order numerical approximations for the one- and two-dimensional nonlocal wave equations on unbounded spatial domains are considered.…
A sturcture-preserving, upwind-SAV scheme for the degenerate Cahn--Hilliard equation with applications to simulating surface diffusion
Qiong-Ao Huang, Wei Jiang, Jerry Zhijian Yang +1
This paper establishes a structure-preserving numerical scheme for the Cahn--Hilliard equation with degenerate mobility. First, by applying a finite volume method with upwind numer…
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…
Global Optimization via Schr{ö}dinger-F{ö}llmer Diffusion
Yin Dai, Yuling Jiao, Lican Kang +2
We study the problem of finding global minimizers of approximately via sampling from a probability distribution with density $p_σ(x)=…
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…
Convergence Rate Analysis for Deep Ritz Method
Chenguang Duan, Yuling Jiao, Yanming Lai +2
Using deep neural networks to solve PDEs has attracted a lot of attentions recently. However, why the deep learning method works is falling far behind its empirical success. In thi…
Deep Neural Networks with ReLU-Sine-Exponential Activations Break Curse of Dimensionality in Approximation on Hölder Class
Yuling Jiao, Yanming Lai, Xiliang Lu +3
In this paper, we construct neural networks with ReLU, sine and as activation functions. For general continuous defined on with continuity modulus ,…
Generative Learning With Euler Particle Transport
Yuan Gao, Jian Huang, Yuling Jiao +3
We propose an Euler particle transport (EPT) approach for generative learning. The proposed approach is motivated by the problem of finding an optimal transport map from a referenc…
Robust Decoding from Binary Measurements with Cardinality Constraint Least Squares
Zhao Ding, Junjun Huang, Yuling Jiao +2
The main goal of 1-bit compressive sampling is to decode dimensional signals with sparsity level from binary measurements. This is a challenging task due to the presenc…
Calculation of Cauchy stress tensor in molecular dynamics system with a generalized Irving-Kirkwood formulism
Jerry Zhijian Yang, Shukai Du
Irving and Kirkwood formulism (IK formulism) provides a way to compute continuum mechanics quantities at certain location in terms of molecular variables. To make the approach more…
On the Cauchy-Born Approximation at Finite Temperature
Jerry Z. Yang, Chao Mao, Xiantao Li +1
We address several issues regarding the derivation and implementation of the Cauchy-Born approximation of the stress at finite temperature. In particular, an asymptotic expansion i…
Accurate Evaluations of Strain and Stress in Atomistic Simulations of Crystalline Solids
Jerry Zhijian Yang, Xiaojie Wu, Xiantao Li
In this paper, we study the accuracy of Irving-Kirkwood type of formulas for the approximation of continuum quantities from atomistic simulations. Such formulas are derived by expr…