1 citations · 1 across the 4 of their papers we have counts for
5 papers
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…
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…
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…
ReLU Deep Neural Networks and Linear Finite Elements
Juncai He, Lin Li, Jinchao Xu +1
In this paper, we investigate the relationship between deep neural networks (DNN) with rectified linear unit (ReLU) function as the activation function and continuous piecewise lin…