87 citations · 238 across the 24 of their papers we have counts for
25 papers
A Geometric Local Parameterization Method for Generalized Hele-Shaw Free Boundary Problems with Source Terms
Zengyan Zhang, Wenrui Hao, John Harlim
We develop a meshfree numerical framework for Hele--Shaw free boundary problems with surface tension and source terms based on geometric local parameterization and boundary integra…
Homotopy Relaxation Training Algorithms for Infinite-Width Two-Layer ReLU Neural Networks
Yahong Yang, Qipin Chen, Wenrui Hao
In this paper, we present a novel training approach called the Homotopy Relaxation Training Algorithm (HRTA), aimed at accelerating the training process in contrast to traditional…
Gauss Newton method for solving variational problems of PDEs with neural network discretizaitons
Wenrui Hao, Qingguo Hong, Xianlin Jin
The numerical solution of differential equations using machine learning-based approaches has gained significant popularity. Neural network-based discretization has emerged as a pow…
Companion-Based Multi-Level Finite Element Method for Computing Multiple Solutions of Nonlinear Differential Equations
Wenrui Hao, Sun Lee, Young Ju Lee
The use of nonlinear PDEs has led to significant advancements in various fields, such as physics, biology, ecology, and quantum mechanics. However, finding multiple solutions for n…
HomPINNs: homotopy physics-informed neural networks for solving the inverse problems of nonlinear differential equations with multiple solutions
Haoyang Zheng, Yao Huang, Ziyang Huang +2
Due to the complex behavior arising from non-uniqueness, symmetry, and bifurcations in the solution space, solving inverse problems of nonlinear differential equations (DEs) with m…
Deep Learning via Neural Energy Descent
Wenrui Hao, Chunmei Wang, Xingjian Xu +1
This paper proposes the Nerual Energy Descent (NED) via neural network evolution equations for a wide class of deep learning problems. We show that deep learning can be reformulate…
Bifurcation analysis of a free boundary model of vascular tumor growth with a necrotic core and chemotaxis
Min-Jhe Lu, Wenrui Hao, Bei Hu +1
A considerable number of research works has been devoted to the study of tumor models. Several biophysical factors, such as cell proliferation, apoptosis, chemotaxis, angiogenesis…
Bifurcation Analysis Reveals Solution Structures of Phase Field Models
Xinyue Evelyn Zhao, Long-Qing Chen, Wenrui Hao +1
Phase field method is playing an increasingly important role in understanding and predicting morphological evolution in materials and biological systems. Here, we develop a new ana…
Learn bifurcations of nonlinear parametric systems via equation-driven neural networks
Wenrui Hao, Chunyue Zheng
Nonlinear parametric systems have been widely used in modeling nonlinear dynamics in science and engineering. Bifurcation analysis of these nonlinear systems on the parameter space…
Two neural-network-based methods for solving obstacle problems
Xinyue Evelyn Zhao, Wenrui Hao, Bei Hu
Two neural-network-based numerical schemes are proposed to solve the classical obstacle problems. The schemes are based on the universal approximation property of neural networks,…
A Weight Initialization Based on the Linear Product Structure for Neural Networks
Qipin Chen, Wenrui Hao, Juncai He
Weight initialization plays an important role in training neural networks and also affects tremendous deep learning applications. Various weight initialization strategies have alre…
Nonlinear simulation of vascular tumor growth with chemotaxis and the control of necrosis
Min-Jhe Lu, Wenrui Hao, Chun Liu +2
In this paper, we develop a sharp interface tumor growth model in two dimensions to study the effect of both the intratumoral structure using a controlled necrotic core and the ext…
Greedy Training Algorithms for Neural Networks and Applications to PDEs
Jonathan W. Siegel, Qingguo Hong, Xianlin Jin +2
Recently, neural networks have been widely applied for solving partial differential equations (PDEs). Although such methods have been proven remarkably successful on practical engi…
A stochastic homotopy tracking algorithm for parametric systems of nonlinear equations
Wenrui Hao, Chunyue Zheng
The homotopy continuation method has been widely used in solving parametric systems of nonlinear equations. But it can be very expensive and inefficient due to singularities during…
Power Series Expansion Neural Network
Qipin Chen, Wenrui Hao, Juncai He
In this paper, we develop a new neural network family based on power series expansion, which is proved to achieve a better approximation accuracy in comparison with existing neural…
Projection based model reduction for the immersed boundary method
Yushuang Luo, Xiantao Li, Wenrui Hao
Fluid-structure interactions are central to many bio-molecular processes, and they impose a great challenge for computational and modeling methods. In this paper, we consider the i…
Convergence analysis of neural networks for solving a free boundary system
Xinyue Evelyn Zhao, Wenrui Hao, Bei Hu
Free boundary problems deal with systems of partial differential equations, where the domain boundaries are apriori unknown. Due to this special characteristic, it is challenging t…
Bifurcation analysis of a free boundary model of plaque formation associated with the cholesterol ratio
Wenrui Hao, Chunyue Zheng
The low-density lipoprotein (LDL)/high-density lipoprotein (HDL)-cholesterol ratio has been shown a high correlation with the cardiovascular risk assessment. Is it possible to quan…
An adaptive homotopy method for computing bifurcations of nonlinear parametric systems
Wenrui Hao, Chunyue Zheng
In this paper, we present an adaptive step-size homotopy tracking method for computing bifurcation points of nonlinear systems. There are four components in this new method: 1) an…
A machine learning method correlating pulse pressure wave data with pregnancy
Jianhong Chen, Huang Huang, Wenrui Hao +1
Pulse feeling, representing the tactile arterial palpation of the heartbeat, has been widely used in traditional Chinese medicine (TCM) to diagnose various diseases. The quantitati…
A homotopy training algorithm for fully connected neural networks
Qipin Chen, Wenrui Hao
In this paper, we present a Homotopy Training Algorithm (HTA) to solve optimization problems arising from fully connected neural networks with complicated structures. The HTA dynam…
An Equation-By-Equation Method for Solving the Multidimensional Moment Constrained Maximum Entropy Problem
Wenrui Hao, John Harlim
An equation-by-equation (EBE) method is proposed to solve a system of nonlinear equations arising from the moment constrained maximum entropy problem of multidimensional variables.…
Counting solutions of the Bethe equations of the quantum group invariant open XXZ chain at roots of unity
Azat M. Gainutdinov, Wenrui Hao, Rafael I. Nepomechie +1
We consider the sl(2)_q-invariant open spin-1/2 XXZ quantum spin chain of finite length N. For the case that q is a root of unity, we propose a formula for the number of admissible…
Singular solutions, repeated roots and completeness for higher-spin chains
Wenrui Hao, Rafael I. Nepomechie, Andrew J. Sommese
We investigate the completeness of the solutions of the Bethe equations for the integrable spin-s isotropic (XXX) spin chain with periodic boundary conditions. Solutions containing…