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2020 – today
- 2025
[j43]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. J. Comput. Phys. 521: 113565 (2025)- 2024
- [j42]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: 162-173 (2024) - [j41]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: 112751 (2024) - [j40]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): 56 (2024) - [j39]Wenrui Hao, Qingguo Hong, Xianlin Jin:
Gauss Newton Method for Solving Variational Problems of PDEs with Neural Network Discretizaitons. J. Sci. Comput. 100(1): 17 (2024) - [i25]Lin Li, Yangyi Ye, Wenrui Hao, Huiyuan Li:
An Adaptive Orthogonal Basis Method for Computing Multiple Solutions of Differential Equations with polynomial nonlinearities. CoRR abs/2402.18793 (2024) - [i24]Wenrui Hao, Xinliang Liu, Yahong Yang:
Newton Informed Neural Operator for Computing Multiple Solutions of Nonlinear Partials Differential Equations. CoRR abs/2405.14096 (2024) - [i23]Chuqi Chen, Yahong Yang, Yang Xiang, Wenrui Hao:
Automatic Differentiation is Essential in Training Neural Networks for Solving Differential Equations. CoRR abs/2405.14099 (2024) - [i22]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 abs/2406.18393 (2024) - [i21]Wenrui Hao, Chun Liu, Yiwei Wang, Yahong Yang:
On pattern formation in the thermodynamically-consistent variational Gray-Scott model. CoRR abs/2409.04663 (2024) - 2023
- [j38]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: 112084 (2023) - [i20]Wenrui Hao, Chunmei Wang, Xingjian Xu, Haizhao Yang:
Deep Learning via Neural Energy Descent. CoRR abs/2302.10424 (2023) - [i19]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 abs/2304.02811 (2023) - [i18]Wenrui Hao, Sun Lee, Young Ju Lee:
Companion-Based Multi-Level Finite Element Method for Computing Multiple Solutions of Nonlinear Differential Equations. CoRR abs/2305.04162 (2023) - [i17]Wenrui Hao, Qingguo Hong, Xianlin Jin, Yiran Wang:
Gauss Newton method for solving variational problems of PDEs with neural network discretizaitons. CoRR abs/2306.08727 (2023) - [i16]Yahong Yang, Qipin Chen, Wenrui Hao:
Homotopy Relaxation Training Algorithms for Infinite-Width Two-Layer ReLU Neural Networks. CoRR abs/2309.15244 (2023) - [i15]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 abs/2311.09866 (2023) - 2022
- [j37]Qipin Chen, Wenrui Hao, Juncai He:
A weight initialization based on the linear product structure for neural networks. Appl. Math. Comput. 415: 126722 (2022) - [j36]Wenrui Hao:
An adaptive homotopy tracking algorithm for solving nonlinear parametric systems with applications in nonlinear ODEs. Appl. Math. Lett. 125: 107767 (2022) - [j35]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: 62-73 (2022) - [j34]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 L. 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 F. 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) - [j33]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: 111153 (2022) - [j32]Qipin Chen, Wenrui Hao, Juncai He:
Power series expansion neural network. J. Comput. Sci. 59: 101552 (2022) - [j31]Qipin Chen, Wenrui Hao:
Randomized Newton's Method for Solving Differential Equations Based on the Neural Network Discretization. J. Sci. Comput. 92(2): 49 (2022) - [j30]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) - [j29]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): 1010481 (2022) - [i14]Yushuang Luo, Xiantao Li, Wenrui Hao:
Stability Preserving Data-driven Models With Latent Dynamics. CoRR abs/2204.11744 (2022) - [i13]Xinyue Evelyn Zhao, Long-Qing Chen, Wenrui Hao, Yanxiang Zhao:
Bifurcation Analysis Reveals Solution Structures of Phase Field Models. CoRR abs/2210.06691 (2022) - 2021
- [j28]Wenrui Hao:
A gradient descent method for solving a system of nonlinear equations. Appl. Math. Lett. 112: 106739 (2021) - [j27]Xinyue Evelyn Zhao, Wenrui Hao, Bei Hu:
Convergence analysis of neural networks for solving a free boundary problem. Comput. Math. Appl. 93: 144-155 (2021) - [j26]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: 110181 (2021) - [j25]Wenrui Hao, Chunyue Zheng:
A Stochastic Homotopy Tracking Algorithm for Parametric Systems of Nonlinear Equations. J. Sci. Comput. 87(3): 87 (2021) - [i12]Yushuang Luo, Xiantao Li, Wenrui Hao:
Projection based model reduction for the immersed boundary method. CoRR abs/2101.12088 (2021) - [i11]Qipin Chen, Wenrui Hao, Juncai He:
Power series expansion neural network. CoRR abs/2102.13221 (2021) - [i10]Wenrui Hao, Chunyue Zheng:
A stochastic homotopy tracking algorithm for parametric systems of nonlinear equations. CoRR abs/2104.05667 (2021) - [i9]Wenrui Hao, Xianlin Jin, Jonathan W. Siegel, Jinchao Xu:
An efficient greedy training algorithm for neural networks and applications in PDEs. CoRR abs/2107.04466 (2021) - [i8]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 abs/2107.11701 (2021) - [i7]Qipin Chen, Wenrui Hao, Juncai He:
A Weight Initialization Based on the Linear Product Structure for Neural Networks. CoRR abs/2109.00125 (2021) - [i6]Xinyue Evelyn Zhao, Wenrui Hao, Bei Hu:
Two neural-network-based methods for solving obstacle problems. CoRR abs/2111.01761 (2021) - [i5]Wenrui Hao, Chunyue Zheng:
Learn bifurcations of nonlinear parametric systems via equation-driven neural networks. CoRR abs/2112.07751 (2021) - 2020
- [j24]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): 19 (2020) - [j23]Wenrui Hao, Chunyue Zheng:
An Adaptive Homotopy Method for Computing Bifurcations of Nonlinear Parametric Systems. J. Sci. Comput. 82(3): 53 (2020) - [i4]Wenrui Hao, Chunyue Zheng:
An adaptive homotopy method for computing bifurcations of nonlinear parametric systems. CoRR abs/2002.03460 (2020) - [i3]Xinyue Evelyn Zhao, Wenrui Hao, Bei Hu:
Convergence analysis of neural networks for solving a free boundary system. CoRR abs/2011.00315 (2020)
2010 – 2019
- 2019
- [j22]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: 6216530:1-6216530:8 (2019) - [i2]Jianhong Chen, Huang Huang, Wenrui Hao, Jinchao Xu:
A machine learning method correlating pulse pressure wave data with pregnancy. CoRR abs/1910.01726 (2019) - [i1]Qipin Chen, Wenrui Hao:
A randomized Newton's method for solving differential equations based on the neural network discretization. CoRR abs/1912.03196 (2019) - 2018
- [j21]Wenrui Hao, Bei Hu, Shuwang Li, Lingyu Song:
Convergence of boundary integral method for a free boundary system. J. Comput. Appl. Math. 334: 128-157 (2018) - [j20]Wenrui Hao:
A Homotopy Method for Parameter Estimation of Nonlinear Differential Equations with Multiple Optima. J. Sci. Comput. 74(3): 1314-1324 (2018) - [j19]Yingwei Wang, Wenrui Hao, Guang Lin:
Two-Level Spectral Methods for Nonlinear Elliptic Equations with Multiple Solutions. SIAM J. Sci. Comput. 40(4): B1180-B1205 (2018) - 2017
- [j18]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): 1215-1225 (2017) - [j17]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): 10:1-10:30 (2017) - 2016
- [j16]Wenrui Hao, Avner Friedman:
Mathematical model on Alzheimer's disease. BMC Syst. Biol. 10: 108:1-108:18 (2016) - 2015
- [j15]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: 345-362 (2015) - 2014
- [j14]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: 181-190 (2014) - [c2]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: 175-182 - 2013
- [j13]Wenrui Hao, Shaohong Zhu:
Domain decomposition schemes with high-order accuracy and unconditional stability. Appl. Math. Comput. 219(11): 6170-6181 (2013) - [j12]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): 1401-1413 (2013) - [j11]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): 326-334 (2013) - [j10]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: 332-346 (2013) - [j9]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): 350-365 (2013) - [j8]Wenrui Hao, Zhenzhou Lu, Pengfei Wei:
Uncertainty importance measure for models with correlated normal variables. Reliab. Eng. Syst. Saf. 112: 48-58 (2013) - [j7]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): 5:1-5:16 (2013) - 2012
- [j6]Pengfei Wei, Zhenzhou Lu, Wenrui Hao, Jun Feng, Bintuan Wang:
Efficient sampling methods for global reliability sensitivity analysis. Comput. Phys. Commun. 183(8): 1728-1743 (2012) - [j5]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): 395-413 (2012) - [j4]Wenrui Hao, Zhenzhou Lu, Longfei Tian:
Importance measure of correlated normal variables and its sensitivity analysis. Reliab. Eng. Syst. Saf. 99: 151-160 (2012) - 2011
- [j3]Wenrui Hao, Jonathan D. Hauenstein, Bei Hu, Andrew J. Sommese:
A three-dimensional steady-state tumor system. Appl. Math. Comput. 218(6): 2661-2669 (2011) - 2010
- [c1]Wenrui Hao, Chang Liu:
High-order Parallel Iterative Method For The Heat Equations. CSC 2010: 243-250
2000 – 2009
- 2009
- [j2]Wenrui Hao, Shaohong Zhu:
Parallel iterative methods for parabolic equations. Int. J. Comput. Math. 86(3): 431-440 (2009) - [j1]Fasheng Sun, Min-Qian Liu, Wenrui Hao:
An algorithmic approach to finding factorial designs with generalized minimum aberration. J. Complex. 25(1): 75-84 (2009)
Coauthor Index
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