Wenrui Hao

Publication Activity (10 Years)

Years Active: 2009-2024
Publications (10 Years): 51

Top Topics

Differential Equations

Series Expansion

Top Venues

J. Sci. Comput.

J. Comput. Phys.

Comput. Math. Appl.

Publications

Wenrui Hao, Jonathan D. Hauenstein, Margaret H. Regan, Tingting Tang
A Numerical Method for Solving Elliptic Equations on Real Closed Algebraic Curves and Surfaces. J. Sci. Comput. 99 (2) (2024)
Wenrui Hao, Sun Lee, Young Ju Lee
Companion-based multi-level finite element method for computing multiple solutions of nonlinear differential equations. Comput. Math. Appl. 168 (2024)
Wenrui Hao, Sun Lee, Xiaofeng Xu, Zhiliang Xu
Stability and Robustness of Time-discretization Schemes for the Allen-Cahn Equation via Bifurcation and Perturbation Analysis. CoRR (2024)
Chuqi Chen, Yahong Yang, Yang Xiang, Wenrui Hao
Automatic Differentiation is Essential in Training Neural Networks for Solving Differential Equations. CoRR (2024)
Wenrui Hao, Qingguo Hong, Xianlin Jin
Gauss Newton Method for Solving Variational Problems of PDEs with Neural Network Discretizaitons. J. Sci. Comput. 100 (1) (2024)
Lin Li, Yangyi Ye, Wenrui Hao, Huiyuan Li
An Adaptive Orthogonal Basis Method for Computing Multiple Solutions of Differential Equations with polynomial nonlinearities. CoRR (2024)
Wenrui Hao, Xinliang Liu, Yahong Yang
Newton Informed Neural Operator for Computing Multiple Solutions of Nonlinear Partials Differential Equations. CoRR (2024)
Haoyang Zheng, Yao Huang, Ziyang Huang, Wenrui Hao, Guang Lin
HomPINNs: Homotopy physics-informed neural networks for solving the inverse problems of nonlinear differential equations with multiple solutions. J. Comput. Phys. 500 (2024)
Wenrui Hao, Chunmei Wang, Xingjian Xu, Haizhao Yang
Deep Learning via Neural Energy Descent. CoRR (2023)
Wenrui Hao, Qingguo Hong, Xianlin Jin, Yiran Wang
Gauss Newton method for solving variational problems of PDEs with neural network discretizaitons. CoRR (2023)
Wenrui Hao, Sun Lee, Young Ju Lee
Companion-Based Multi-Level Finite Element Method for Computing Multiple Solutions of Nonlinear Differential Equations. CoRR (2023)
Wenrui Hao, Jonathan D. Hauenstein, Margaret H. Regan, Tingting Tang
A numerical method for solving elliptic equations on real closed algebraic curves and surfaces. CoRR (2023)
Haoyang Zheng, Yao Huang, Ziyang Huang, Wenrui Hao, Guang Lin
HomPINNs: homotopy physics-informed neural networks for solving the inverse problems of nonlinear differential equations with multiple solutions. CoRR (2023)
Yahong Yang, Qipin Chen, Wenrui Hao
Homotopy Relaxation Training Algorithms for Infinite-Width Two-Layer ReLU Neural Networks. CoRR (2023)
Jonathan W. Siegel, Qingguo Hong, Xianlin Jin, Wenrui Hao, Jinchao Xu
Greedy training algorithms for neural networks and applications to PDEs. J. Comput. Phys. 484 (2023)
Yushuang Luo, Xiantao Li, Wenrui Hao
Stability Preserving Data-driven Models With Latent Dynamics. CoRR (2022)
Wenrui Hao
An adaptive homotopy tracking algorithm for solving nonlinear parametric systems with applications in nonlinear ODEs. Appl. Math. Lett. 125 (2022)
Qipin Chen, Wenrui Hao, Juncai He
A weight initialization based on the linear product structure for neural networks. Appl. Math. Comput. 415 (2022)
Min-Jhe Lu, Wenrui Hao, Chun Liu, John S. Lowengrub, Shuwang Li
Nonlinear simulation of vascular tumor growth with chemotaxis and the control of necrosis. J. Comput. Phys. 459 (2022)
Eric A. Stahlberg, Mohamed Abdel-Rahman, Boris Aguilar, Alireza Asadpoure, Robert A. Beckman, Lynn L. Borkon, Jeffrey N. Bryan, Colleen M. Cebulla, Young Hwan Chang, Ansu Chatterjee, Jun Deng, Sepideh Dolatshahi, Olivier Gevaert, Emily J. Greenspan, Wenrui Hao, Tina Hernandez-Boussard, Pamela R. Jackson, Marieke Kuijjer, Adrian Lee, Paul Macklin, Subha Madhavan, Matthew D. McCoy, Navid Mohammad Mirzaei, Talayeh Razzaghi, Heber L. Rocha, Leili Shahriyari, Ilya Shmulevich, Daniel G. Stover, Yi Sun, Tanveer Syeda-Mahmood, Jinhua Wang, Qi Wang, Ioannis K. Zervantonakis
Exploring approaches for predictive cancer patient digital twins: Opportunities for collaboration and innovation. Frontiers Digit. Health 4 (2022)
Haoyang Zheng, Jeffrey R. Petrella, P. Murali Doraiswamy, Guang Lin, Wenrui Hao
Data-driven causal model discovery and personalized prediction in Alzheimer's disease. npj Digit. Medicine 5 (2022)
Xinyue Evelyn Zhao, Long-Qing Chen, Wenrui Hao, Yanxiang Zhao
Bifurcation Analysis Reveals Solution Structures of Phase Field Models. CoRR (2022)
Qipin Chen, Wenrui Hao, Juncai He
Power series expansion neural network. J. Comput. Sci. 59 (2022)
Wenrui Hao, Suzanne Lenhart, Jeffrey R. Petrella
Optimal anti-amyloid-beta therapy for Alzheimer's disease via a personalized mathematical model. PLoS Comput. Biol. 18 (9) (2022)
Qipin Chen, Wenrui Hao
Randomized Newton's Method for Solving Differential Equations Based on the Neural Network Discretization. J. Sci. Comput. 92 (2) (2022)
Yao Huang, Wenrui Hao, Guang Lin
HomPINNs: Homotopy physics-informed neural networks for learning multiple solutions of nonlinear elliptic differential equations. Comput. Math. Appl. 121 (2022)
Wenrui Hao, Xianlin Jin, Jonathan W. Siegel, Jinchao Xu
An efficient greedy training algorithm for neural networks and applications in PDEs. CoRR (2021)
Qipin Chen, Wenrui Hao, Juncai He
A Weight Initialization Based on the Linear Product Structure for Neural Networks. CoRR (2021)
Wenrui Hao, Chunyue Zheng
A stochastic homotopy tracking algorithm for parametric systems of nonlinear equations. CoRR (2021)
Xinyue Evelyn Zhao, Wenrui Hao, Bei Hu
Convergence analysis of neural networks for solving a free boundary problem. Comput. Math. Appl. 93 (2021)
Yushuang Luo, Xiantao Li, Wenrui Hao
Projection based model reduction for the immersed boundary method. CoRR (2021)
Wenrui Hao, Chunyue Zheng
A Stochastic Homotopy Tracking Algorithm for Parametric Systems of Nonlinear Equations. J. Sci. Comput. 87 (3) (2021)
Wenrui Hao, Chunyue Zheng
Learn bifurcations of nonlinear parametric systems via equation-driven neural networks. CoRR (2021)
Wenrui Hao
A gradient descent method for solving a system of nonlinear equations. Appl. Math. Lett. 112 (2021)
Qipin Chen, Wenrui Hao, Juncai He
Power series expansion neural network. CoRR (2021)
Xinyue Evelyn Zhao, Wenrui Hao, Bei Hu
Two neural-network-based methods for solving obstacle problems. CoRR (2021)
Wenrui Hao, Pengtao Sun, Jinchao Xu, Lian Zhang
Multiscale and monolithic arbitrary Lagrangian-Eulerian finite element method for a hemodynamic fluid-structure interaction problem involving aneurysms. J. Comput. Phys. 433 (2021)
Min-Jhe Lu, Wenrui Hao, Chun Liu, John S. Lowengrub, Shuwang Li
Nonlinear simulation of vascular tumor growth with chemotaxis and the control of necrosis. CoRR (2021)
Wenrui Hao, Chunyue Zheng
An Adaptive Homotopy Method for Computing Bifurcations of Nonlinear Parametric Systems. J. Sci. Comput. 82 (3) (2020)
Wenrui Hao, Jan S. Hesthaven, Guang Lin, Bin Zheng
A Homotopy Method with Adaptive Basis Selection for Computing Multiple Solutions of Differential Equations. J. Sci. Comput. 82 (1) (2020)
Wenrui Hao, Chunyue Zheng
An adaptive homotopy method for computing bifurcations of nonlinear parametric systems. CoRR (2020)
Xinyue Evelyn Zhao, Wenrui Hao, Bei Hu
Convergence analysis of neural networks for solving a free boundary system. CoRR (2020)
Jeffrey R. Petrella, Wenrui Hao, Adithi Rao, P. Murali Doraiswamy
Computational Causal Modeling of the Dynamic Biomarker Cascade in Alzheimer's Disease. Comput. Math. Methods Medicine 2019 (2019)
Jianhong Chen, Huang Huang, Wenrui Hao, Jinchao Xu
A machine learning method correlating pulse pressure wave data with pregnancy. CoRR (2019)
Qipin Chen, Wenrui Hao
A randomized Newton's method for solving differential equations based on the neural network discretization. CoRR (2019)
Yingwei Wang, Wenrui Hao, Guang Lin
Two-Level Spectral Methods for Nonlinear Elliptic Equations with Multiple Solutions. SIAM J. Sci. Comput. 40 (4) (2018)
Wenrui Hao, Bei Hu, Shuwang Li, Lingyu Song
Convergence of boundary integral method for a free boundary system. J. Comput. Appl. Math. 334 (2018)
Wenrui Hao
A Homotopy Method for Parameter Estimation of Nonlinear Differential Equations with Multiple Optima. J. Sci. Comput. 74 (3) (2018)
Daniel A. Brake, Daniel J. Bates, Wenrui Hao, Jonathan D. Hauenstein, Andrew J. Sommese, Charles W. Wampler
Algorithm 976: Bertini_real: Numerical Decomposition of Real Algebraic Curves and Surfaces. ACM Trans. Math. Softw. 44 (1) (2017)
Haiying Quan, Wenrui Hao, Lu Li, Ming Sun, Kuan Zhang
Algorithm to improve accuracy of energy expended in a room calorimeter. Medical Biol. Eng. Comput. 55 (8) (2017)
Wenrui Hao, Avner Friedman
Mathematical model on Alzheimer's disease. BMC Syst. Biol. 10 (2016)
Wenrui Hao, Zhiliang Xu, Chun Liu, Guang Lin
A fictitious domain method with a hybrid cell model for simulating motion of cells in fluid flow. J. Comput. Phys. 280 (2015)
Wenrui Hao, Jonathan D. Hauenstein, Bei Hu, Andrew J. Sommese
A bootstrapping approach for computing multiple solutions of differential equations. J. Comput. Appl. Math. 258 (2014)
Daniel A. Brake, Daniel J. Bates, Wenrui Hao, Jonathan D. Hauenstein, Andrew J. Sommese, Charles W. Wampler
Bertini_real: Software for One- and Two-Dimensional Real Algebraic Sets. ICMS (2014)
Wenrui Hao, Zhenzhou Lu, Luyi Li
A new interpretation and validation of variance based importance measures for models with correlated inputs. Comput. Phys. Commun. 184 (5) (2013)
Wenrui Hao, Zhenzhou Lu, Pengfei Wei
Uncertainty importance measure for models with correlated normal variables. Reliab. Eng. Syst. Saf. 112 (2013)
Wenrui Hao, Bei Hu, Andrew J. Sommese
Cell Cycle Control and Bifurcation for a Free Boundary Problem Modeling Tissue Growth. J. Sci. Comput. 56 (2) (2013)
Wenrui Hao, Shaohong Zhu
Domain decomposition schemes with high-order accuracy and unconditional stability. Appl. Math. Comput. 219 (11) (2013)
Wenrui Hao, Jonathan D. Hauenstein, Chi-Wang Shu, Andrew J. Sommese, Zhiliang Xu, Yong-Tao Zhang
A homotopy method based on WENO schemes for solving steady state problems of hyperbolic conservation laws. J. Comput. Phys. 250 (2013)
Wenrui Hao, Jonathan D. Hauenstein, Bei Hu, Timothy M. McCoy, Andrew J. Sommese
Computing steady-state solutions for a free boundary problem modeling tumor growth by Stokes equation. J. Comput. Appl. Math. 237 (1) (2013)
Wenrui Hao, Andrew J. Sommese, Zhonggang Zeng
Algorithm 931: An algorithm and software for computing multiplicity structures at zeros of nonlinear systems. ACM Trans. Math. Softw. 40 (1) (2013)
Wenrui Hao, Jonathan D. Hauenstein, Bei Hu, Yuan Liu, Andrew J. Sommese, Yong-Tao Zhang
Continuation Along Bifurcation Branches for a Tumor Model with a Necrotic Core. J. Sci. Comput. 53 (2) (2012)
Pengfei Wei, Zhenzhou Lu, Wenrui Hao, Jun Feng, Bintuan Wang
Efficient sampling methods for global reliability sensitivity analysis. Comput. Phys. Commun. 183 (8) (2012)
Wenrui Hao, Zhenzhou Lu, Longfei Tian
Importance measure of correlated normal variables and its sensitivity analysis. Reliab. Eng. Syst. Saf. 99 (2012)
Wenrui Hao, Jonathan D. Hauenstein, Bei Hu, Andrew J. Sommese
A three-dimensional steady-state tumor system. Appl. Math. Comput. 218 (6) (2011)
Wenrui Hao, Chang Liu
High-order Parallel Iterative Method For The Heat Equations. CSC (2010)
Wenrui Hao, Shaohong Zhu
Parallel iterative methods for parabolic equations. Int. J. Comput. Math. 86 (3) (2009)
Fasheng Sun, Min-Qian Liu, Wenrui Hao
An algorithmic approach to finding factorial designs with generalized minimum aberration. J. Complex. 25 (1) (2009)