Parallel iterative methods for parabolic equations. - Wenrui Hao; Shaohong Zhu (Int. J. Comput. Math., 2009)

An algorithmic approach to finding factorial designs with generalized minimum aberration. - Fasheng Sun; Min-Qian Liu; Wenrui Hao (J. Complex., 2009)

High-order Parallel Iterative Method For The Heat Equations. - Wenrui Hao; Chang Liu (CSC, 2010)

A three-dimensional steady-state tumor system. - Wenrui Hao; Jonathan D. Hauenstein; Bei Hu; Andrew J. Sommese (Appl. Math. Comput., 2011)

Efficient sampling methods for global reliability sensitivity analysis. - Pengfei Wei 002; Zhenzhou Lu; Wenrui Hao; Jun Feng; Bintuan Wang (Comput. Phys. Commun., 2012)

Continuation Along Bifurcation Branches for a Tumor Model with a Necrotic Core. - Wenrui Hao; Jonathan D. Hauenstein; Bei Hu; Yuan Liu 018; Andrew J. Sommese; Yong-Tao Zhang (J. Sci. Comput., 2012)

Importance measure of correlated normal variables and its sensitivity analysis. - Wenrui Hao; Zhenzhou Lu; Longfei Tian (Reliab. Eng. Syst. Saf., 2012)

Domain decomposition schemes with high-order accuracy and unconditional stability. - Wenrui Hao; Shaohong Zhu (Appl. Math. Comput., 2013)

A new interpretation and validation of variance based importance measures for models with correlated inputs. - Wenrui Hao; Zhenzhou Lu; Luyi Li (Comput. Phys. Commun., 2013)

Computing steady-state solutions for a free boundary problem modeling tumor growth by Stokes equation. - Wenrui Hao; Jonathan D. Hauenstein; Bei Hu; Timothy M. McCoy; Andrew J. Sommese (J. Comput. Appl. Math., 2013)

A homotopy method based on WENO schemes for solving steady state problems of hyperbolic conservation laws. - Wenrui Hao; Jonathan D. Hauenstein; Chi-Wang Shu; Andrew J. Sommese; Zhiliang Xu; Yong-Tao Zhang (J. Comput. Phys., 2013)

Cell Cycle Control and Bifurcation for a Free Boundary Problem Modeling Tissue Growth. - Wenrui Hao; Bei Hu; Andrew J. Sommese (J. Sci. Comput., 2013)

Uncertainty importance measure for models with correlated normal variables. - Wenrui Hao; Zhenzhou Lu; Pengfei Wei 002 (Reliab. Eng. Syst. Saf., 2013)

Algorithm 931: An algorithm and software for computing multiplicity structures at zeros of nonlinear systems. - Wenrui Hao; Andrew J. Sommese; Zhonggang Zeng (ACM Trans. Math. Softw., 2013)

Bertini_real: Software for One- and Two-Dimensional Real Algebraic Sets. - Daniel A. Brake; Daniel J. Bates; Wenrui Hao; Jonathan D. Hauenstein; Andrew J. Sommese; Charles W. Wampler (ICMS, 2014)

A bootstrapping approach for computing multiple solutions of differential equations. - Wenrui Hao; Jonathan D. Hauenstein; Bei Hu; Andrew J. Sommese (J. Comput. Appl. Math., 2014)

A fictitious domain method with a hybrid cell model for simulating motion of cells in fluid flow. - Wenrui Hao; Zhiliang Xu; Chun Liu 009; Guang Lin 001 (J. Comput. Phys., 2015)

Mathematical model on Alzheimer's disease. - Wenrui Hao; Avner Friedman (BMC Syst. Biol., 2016)

Algorithm to improve accuracy of energy expended in a room calorimeter. - Haiying Quan; Wenrui Hao; Lu Li; Ming Sun; Kuan Zhang (Medical Biol. Eng. Comput., 2017)

Algorithm 976: Bertini_real: Numerical Decomposition of Real Algebraic Curves and Surfaces. - Daniel A. Brake; Daniel J. Bates; Wenrui Hao; Jonathan D. Hauenstein; Andrew J. Sommese; Charles W. Wampler (ACM Trans. Math. Softw., 2017)

Convergence of boundary integral method for a free boundary system. - Wenrui Hao; Bei Hu; Shuwang Li; Lingyu Song (J. Comput. Appl. Math., 2018)

A Homotopy Method for Parameter Estimation of Nonlinear Differential Equations with Multiple Optima. - Wenrui Hao (J. Sci. Comput., 2018)

Two-Level Spectral Methods for Nonlinear Elliptic Equations with Multiple Solutions. - Yingwei Wang; Wenrui Hao; Guang Lin 001 (SIAM J. Sci. Comput., 2018)

Computational Causal Modeling of the Dynamic Biomarker Cascade in Alzheimer's Disease. - Jeffrey R. Petrella; Wenrui Hao; Adithi Rao; P. Murali Doraiswamy (Comput. Math. Methods Medicine, 2019)

A machine learning method correlating pulse pressure wave data with pregnancy. - Jianhong Chen; Huang Huang; Wenrui Hao; Jinchao Xu (CoRR, 2019)

Convergence analysis of neural networks for solving a free boundary system. - Xinyue Evelyn Zhao; Wenrui Hao; Bei Hu (CoRR, 2020)

A Homotopy Method with Adaptive Basis Selection for Computing Multiple Solutions of Differential Equations. - Wenrui Hao; Jan S. Hesthaven; Guang Lin 001; Bin Zheng (J. Sci. Comput., 2020)

An Adaptive Homotopy Method for Computing Bifurcations of Nonlinear Parametric Systems. - Wenrui Hao; Chunyue Zheng (J. Sci. Comput., 2020)

A gradient descent method for solving a system of nonlinear equations. - Wenrui Hao (Appl. Math. Lett., 2021)

Convergence analysis of neural networks for solving a free boundary problem. - Xinyue Evelyn Zhao; Wenrui Hao; Bei Hu (Comput. Math. Appl., 2021)

Projection based model reduction for the immersed boundary method. - Yushuang Luo; Xiantao Li; Wenrui Hao (CoRR, 2021)

An efficient greedy training algorithm for neural networks and applications in PDEs. - Wenrui Hao; Xianlin Jin; Jonathan W. Siegel; Jinchao Xu (CoRR, 2021)

Two neural-network-based methods for solving obstacle problems. - Xinyue Evelyn Zhao; Wenrui Hao; Bei Hu (CoRR, 2021)

Learn bifurcations of nonlinear parametric systems via equation-driven neural networks. - Wenrui Hao; Chunyue Zheng (CoRR, 2021)

Multiscale and monolithic arbitrary Lagrangian-Eulerian finite element method for a hemodynamic fluid-structure interaction problem involving aneurysms. - Wenrui Hao; Pengtao Sun; Jinchao Xu; Lian Zhang (J. Comput. Phys., 2021)

A Stochastic Homotopy Tracking Algorithm for Parametric Systems of Nonlinear Equations. - Wenrui Hao; Chunyue Zheng (J. Sci. Comput., 2021)

A weight initialization based on the linear product structure for neural networks. - Qipin Chen; Wenrui Hao; Juncai He 001 (Appl. Math. Comput., 2022)

An adaptive homotopy tracking algorithm for solving nonlinear parametric systems with applications in nonlinear ODEs. - Wenrui Hao (Appl. Math. Lett., 2022)

HomPINNs: Homotopy physics-informed neural networks for learning multiple solutions of nonlinear elliptic differential equations. - Yao Huang; Wenrui Hao; Guang Lin 001 (Comput. Math. Appl., 2022)

Stability Preserving Data-driven Models With Latent Dynamics. - Yushuang Luo; Xiantao Li; Wenrui Hao (CoRR, 2022)

Bifurcation Analysis Reveals Solution Structures of Phase Field Models. - Xinyue Evelyn Zhao; Long-Qing Chen; Wenrui Hao; Yanxiang Zhao (CoRR, 2022)

Exploring approaches for predictive cancer patient digital twins: Opportunities for collaboration and innovation. - 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; et al. (Frontiers Digit. Health, 2022)

Nonlinear simulation of vascular tumor growth with chemotaxis and the control of necrosis. - Min-Jhe Lu; Wenrui Hao; Chun Liu 009; John S. Lowengrub; Shuwang Li (J. Comput. Phys., 2022)

Power series expansion neural network. - Qipin Chen; Wenrui Hao; Juncai He 001 (J. Comput. Sci., 2022)

Randomized Newton's Method for Solving Differential Equations Based on the Neural Network Discretization. - Qipin Chen; Wenrui Hao (J. Sci. Comput., 2022)

Data-driven causal model discovery and personalized prediction in Alzheimer's disease. - Haoyang Zheng; Jeffrey R. Petrella; P. Murali Doraiswamy; Guang Lin 001; Wenrui Hao (npj Digit. Medicine, 2022)

Optimal anti-amyloid-beta therapy for Alzheimer's disease via a personalized mathematical model. - Wenrui Hao; Suzanne Lenhart; Jeffrey R. Petrella (PLoS Comput. Biol., 2022)

Deep Learning via Neural Energy Descent. - Wenrui Hao; Chunmei Wang; Xingjian Xu; Haizhao Yang (CoRR, 2023)

Gauss Newton method for solving variational problems of PDEs with neural network discretizaitons. - Wenrui Hao; Qingguo Hong; Xianlin Jin; Yiran Wang (CoRR, 2023)

Greedy training algorithms for neural networks and applications to PDEs. - Jonathan W. Siegel; Qingguo Hong; Xianlin Jin; Wenrui Hao; Jinchao Xu (J. Comput. Phys., 2023)

Newton Informed Neural Operator for Solving Nonlinear Partial Differential Equations. - Wenrui Hao; Xinliang Liu; Yahong Yang (NeurIPS, 2024)

Companion-based multi-level finite element method for computing multiple solutions of nonlinear differential equations. - Wenrui Hao; Sun Lee; Young Ju Lee (Comput. Math. Appl., 2024)

An Adaptive Orthogonal Basis Method for Computing Multiple Solutions of Differential Equations with polynomial nonlinearities. - Lin Li; Yangyi Ye; Wenrui Hao; Huiyuan Li (CoRR, 2024)

Newton Informed Neural Operator for Computing Multiple Solutions of Nonlinear Partials Differential Equations. - Wenrui Hao; Xinliang Liu; Yahong Yang (CoRR, 2024)

On pattern formation in the thermodynamically-consistent variational Gray-Scott model. - Wenrui Hao; Chun Liu 009; Yiwei Wang; Yahong Yang (CoRR, 2024)

Multiscale Neural Networks for Approximating Green's Functions. - Wenrui Hao; Ruipeng Li; Yuanzhe Xi; Tianshi Xu; Yahong Yang (CoRR, 2024)

HomPINNs: Homotopy physics-informed neural networks for solving the inverse problems of nonlinear differential equations with multiple solutions. - Haoyang Zheng; Yao Huang; Ziyang Huang; Wenrui Hao; Guang Lin 001 (J. Comput. Phys., 2024)

A Numerical Method for Solving Elliptic Equations on Real Closed Algebraic Curves and Surfaces. - Wenrui Hao; Jonathan D. Hauenstein; Margaret H. Regan; Tingting Tang (J. Sci. Comput., 2024)

Gauss Newton Method for Solving Variational Problems of PDEs with Neural Network Discretizaitons. - Wenrui Hao; Qingguo Hong; Xianlin Jin (J. Sci. Comput., 2024)

Stability and robustness of time-discretization schemes for the Allen-Cahn equation via bifurcation and perturbation analysis. - Wenrui Hao; Sun Lee; Xiaofeng Xu; Zhiliang Xu (J. Comput. Phys., 2025)

An imbalanced learning-based sampling method for physics-informed neural networks. - Jiaqi Luo; Yahong Yang; Yuan Yuan; Shixin Xu; Wenrui Hao (J. Comput. Phys., 2025)

Learn Sharp Interface Solution by Homotopy Dynamics. - Chuqi Chen; Yahong Yang; Yang Xiang 002; Wenrui Hao (CoRR, 2025)

Homotopy Relaxation Training Algorithms for Infinite-Width Two-Layer ReLU Neural Networks. - Yahong Yang; Qipin Chen; Wenrui Hao (J. Sci. Comput., 2025)

Error analysis of the diffuse domain finite element method for second order parabolic equations. - Wenrui Hao; Lili Ju; Yuejin Xu (CoRR, 2025)

Accelerating Causal Network Discovery of Alzheimer Disease Biomarkers via Scientific Literature-based Retrieval Augmented Generation. - Xiaofan Zhou; Liangjie Huang; Pinyang Cheng; Wenpeng Yin 001; Rui Zhang 037; Wenrui Hao; Lu Cheng 001 (CoRR, 2025)

ZENN: A Thermodynamics-Inspired Computational Framework for Heterogeneous Data-Driven Modeling. - Shun Wang; Shun-Li Shang; Zi-Kui Liu; Wenrui Hao (CoRR, 2025)

An Efficient Quasi-Newton Method with Tensor Product Implementation for Solving Quasi-Linear Elliptic Equations and Systems. - Wenrui Hao; Sun Lee; Xiangxiong Zhang (J. Sci. Comput., 2025)

Learning Patient-Specific Spatial Biomarker Dynamics via Operator Learning for Alzheimer's Disease Progression. - Jindong Wang; Yutong Mao; Xiao Liu; Wenrui Hao (CoRR, 2025)

Automatic Differentiation is Essential in Training Neural Networks for Solving Differential Equations. - Chuqi Chen; Yahong Yang; Yang Xiang 002; Wenrui Hao (J. Sci. Comput., 2025)