Google scholar profile
Journal publication
- A. Friedman, W. Hao K.-Y. Lam, A cancer model with nonlocal free boundary dynamics, Journal of Mathematical Biology, Vol. 85(5), pp.1-28, (2022).
- X. Zhao, L.-Q. Chen, W. Hao Y. Zhao, Bifurcation Analysis Reveals Solution Structures of Phase Field Models , Communications on Applied Mathematics and Computation, 1-26,(2022)
- W. Hao, S. Lenhart, J. Petrella, Optimal Anti-amyloid-beta Therapy for Alzheimer's Disease via a Personalized Mathematical Model, PLOS Computational Biology, 18(9), e1010481,(2022)
- Y. Luo, X. Li, W. Hao, Stability Preserving Data-driven Models With Latent Dynamics , Chaos, 30(9), (2022) [arxiv]
- X. Zhao, W. Hao B. Hu, Two neural-network-based methods for solving elliptic obstacle problems , Chaos, Solitons & Fractals, Vol. 161, 112313,(2022)
- Y. Huang, W. Hao G. Lin, HomPINNs: Homotopy physics-informed neural networks for learning multiple solutions of nonlinear differential equations , Computers and Mathematics with Applications, Vol. 121 pp. 62-73,(2022)
- H. Zheng, J. Petrella, M. Doraiswamy, G. Lin, W. Hao, Data-driven causal model discovery and personalized prediction in Alzheimer's disease, npj Digital Medicine, Vol. 15 (137),(2022)
- Q. Chen, W. Hao, A randomized Newton's method for solving differential equations based on the neural network discretization, Journal of Scientific Computing, Vol. 87,(2022) [arxiv]
- M.-J. Lu, W. Hao, C. Liu, J. Lowengrub, and S. Li, Nonlinear simulation of vascular tumor growth with chemotaxis and the control of necrosis, Journal of Computational Physics, Vol. 459, 111153, (2022) [arxiv]
- J. Chen, W. Hao, P. Sun, and L. Zhang, Predict blood pressure by photoplethysmogram with the fluid-structure interaction modeling, Communications in Computational Physics, Vol. 31, pp. 1114-1133. (2022)
- Q. Chen, W. Hao, J. He, Power series expansion neural network, Journal of Computational Science, Vol. 92, pp. 1-22, (2022) [arxiv]
- W. Hao, C. Zheng Learn bifurcations of nonlinear parametric systems via equation driven neural networks , Chaos, 32, 011102, (2022) [arxiv]
- Y. Yang, W. Hao, Y.-T. Zhang A continuous finite element method with homotopy vanishing viscosity for solving the static Eikonal equation , Communications in Computational Physics, Vol. 31, pp. 1402-1433, (2022)
- W. Hao, An adaptive homotopy tracking algorithm for solving nonlinear parametric systems with applications in nonlinear ODEs, Applied Mathematics Letters, 107767, (2022)
- Q. Chen, W. Hao, J. He, A weight initialization based on the linear product structure for neural networks, Applied Mathematics and Computation, Volume 415, 126722, (2022) [arxiv]
- Y. Luo, X. Li, W. Hao, Projection based model reduction for the immersed boundary method, International Journal for Numerical Methods in Biomedical Engineering, Vol. 38(2), e3558, (2021) [arxiv]
- W. Hao, C. Zheng, A stochastic homotopy tracking algorithm for parametric systems of nonlinear equations, Journal of Scientific Computing, Vol. 87,(2021) [arxiv]
- X. Zhao, B. Hu, and W. Hao, Convergence analysis of neural networks for solving a free boundary problem, Computers & Mathematics with Applications Vol. 93, pp. 144-155,(2021) [arxiv]
- W. Hao, P. Sun, J. Xu, and L. Zhang, Multiscale and monolithic arbitrary Lagrangian-Eulerian finite element method for a hemodynamic fluid-structure interaction problem involving aneurysms, Journal of Computational Physics, Volume 433, 110181, (2021)
- G. Ke, C. Hans, G. Agarwal, K. Orion, M. Go, and W. Hao, Mathematical model of atherosclerotic aneurysm, Mathematical Biosciences and Engineering, Volume 18(2), 1465-1484, (2021)
- W. Hao, A gradient descent method for solving a system of nonlinear equations , Applied Mathematics Letters, Volume 112, 106739, (2021)
- W. Hao, C. Zheng Bifurcation analysis of a free boundary model of the atherosclerotic plaque formation associated with the cholesterol ratio , Chaos, 30(9), (2020) [arxiv]
- W. Hao, K.-Y. Lam, and Y. Lou Ecological and Evolutionary Dynamics in Advective Environments: Critical Domain Size and Boundary Conditions , DCDS-B, Vol. 26(1), pp. 367-400, (2021)
- G. Karagiannis, W. Hao, G. Lin, Calibrations and validations of biological models with an application on the renal fibrosis, Int J Numer Method Biomed Eng., e3329, (2020)
- W. Hao, C. Zheng, An adaptive homotopy method for computing bifurcations of nonlinear parametric systems, Journal of Scientific Computing, 82(3), 1-19, (2020) [arxiv]
- W. Hao, C. Xue, Spatial pattern formation in reaction-diffusion models: a computational approach, Journal of Mathematical Biology, 80(1), 521-543., (2020)
- W. Hao, J. Hesthaven, G. Lin, B. Zheng, A homotopy method with adaptive basis selection for computing multiple solutions of differential equations, Journal of Scientific Computing, 82(1), 1-19, (2020)
- J. Chen, H. Huang, W. Hao, J. Xu, A machine learning method correlating pulse pressure wave data with pregnancy, International Journal for Numerical Methods in Biomedical Engineering, e3272, (2020)[arxiv]
- Q. Chen, W. Hao, A homotopy training algorithm for fully connected neural networks, Proceedings of the Royal Society A, 475(2231), (2019)[arxiv]
- W. Hao, Y. Yang, Convergence of a homotopy finite element method for computing steady states of Burgers' equation, ESAIM: Mathematical Modelling and Numerical Analysis (ESAIM: M2AN), Vol. 53, Number 5, (2019)
- Y. Wang, W. Hao, G. Lin, Two-level spectral methods for nonlinear elliptic equations with multiple solutions, SIAM Journal on Scientific Computing, Vol. 40(4), B1180-B1205, (2018)
- W. Hao, J. Harlim, An Equation-By-Equation Method for Solving the Multidimensional Moment Constrained Maximum Entropy Problem, Communications in Applied Mathematics and Computational Science, Vol. 13, pp. 189--214, (2018) [arxiv]
- W. Hao, B. Hu, S. Li, L. Song, Convergence of boundary integral method for a free boundary system, Journal of Computational and Applied Mathematics, Vol. 334, pp. 128--157, (2018)
- A. Friedman, W. Hao, The Role of Exosomes in Pancreatic Cancer Microenvironment , Bulletin of Mathematical Biology, Vol. 80, no. 5, pp. 1111-1133. (2018).
- W. Hao, A Homotopy Method for Parameter Estimation of Nonlinear Differential Equations with Multiple Optima, Journal of Scientific Computing, Vol. 74, no. 3, pp. 1314-1324, (2018).
- W. Hao, A. Lam, Y. Lou, Concentration Phenomena in an Integro-PDE Model for Evolution of Conditional Dispersal, Indiana University Mathematics Journal, Vol. 272, pp. 1755-1790, (2017).
- W. Hao, H. Komarb, P. Hart, D. Conwell, G. Lesinskid, A. Friedman Mathematical model of chronic pancreatitis , PNAS, 114 (19), 5011-5016 (2017).
- D. Brake, D. Bates, W. Hao, J. Hauenstein, A. Sommese, C. Wampler, Bertinireal: Numerical decomposition of real algebraic curves and surfaces, ACM Transactions of Mathematical Software, to appear, (2017).
- M. Golubitsky, W. Hao, , K.-Y. Lam, Y. Lou, Dimorphism by Singularity Theory in a Model for River Ecology , Bulletin of Mathematical Biology, 79(5), pp. 1051-1069 (2017).
- W. Hao, S. Gong, S. Wu, J. Xu, M. R. Go, A. Friedman, D. Zhu, A mathematical model of aortic aneurysm formation , PloS One, 12(2), e0170807 (2017).
- A. Friedman, W. Hao, Mathematical modeling of liver fibrosis , Mathematical Biosciences and Engineering, 14(1), pp. 143--164 (2017).
- W. Hao, A. Friedman, Mathematical model on Alzheimer's disease , BMC Syst Biol, 10, 1:108 (2016). (Updated appendeix)
- A.E. Lindsay, W. Hao and A.J. Sommese, Vibrations of thin plates with small clamped patches, Proceedings of the Royal Society A, Volume 471, Issue: 2184, (2016).
- W. Hao, L. Schlesinger, A. Friedman, Modeling granulomas in response to infection in the lung, Plos One, 11, 3:e0148738.(2016).
- W. Hao, C. Marsh, A. Friedman, A Mathematical Model of Idiopathic Pulmonary Fibrosis , Plos One , 10, 9:e0135097, (2015).
- M. Sturrock, W. Hao, J. Schwartzbaum and G. A. Rempala, A mathematical model of pre-diagnostic glioma growth, Journal of Theoretical Biology , Vol. 380, pp. 299--308, (2015).
- A. Friedman, W. Hao and B. Hu, A Free Boundary Problem for Steady Small Plaques in the Arteryand their Stability, Journal of Differential Equations , Vol. 259, pp. 1227--1255, (2015).
- A. Friedman and W. Hao , A mathematical model of atherosclerosis with reverse cholesterol transport and associated risk factors, Bulletin of Mathematical Biology , Vol. 77, pp. 758-781, (2015).
- A. Gainutdinov, W. Hao, R. Nepomechie and A.J. Sommese, Counting solutions of the Bethe equations of the quantum group invariant open XXZ chain at roots of unity, Journal of Physics A: Mathematical and Theoretical , Vol. 48(49), p.494003, (2015).
- W. Hao, Z. Xu, C. Liu and G. Lin, A Fictitious Domain Method with a Hybrid Cell Model for Simulating Motion of Cells in Fluid Flow, Journal of Computational Physics, Volume 280, pp. 345--62, (2015).
- W. Hao, J. D. Hauenstein, B. Hu and A. J. Sommese, A bootstrapping approach for computing multiple solutions of differential equations, Journal of Computational and Applied Mathematics, Volume 258, pp. 181-190 (2014). [pdf]
- W. Hao, E. D. Crouser and A. Friedman, Mathematical model of sarcoidosis , PNAS , Vol. 111 No. 45, pp. 16065--16070, (2014).
- W. Hao, B. H. Rovin and A. Friedman, Mathematical model of renal interstitial fibrosis, PNAS ,Vol. 111 No. 39, pp. 14193--14198, (2014). (Reported at Nature Reviews Nephrology )
- W. Hao and A. Friedman, The LDL-HDL profile determines the risk of atherosclerosis: A mathematical model, PLOS ONE, 9(3): e90497, (2014).
- W. Hao, R. I. Nepomechie and A. J. Sommese, Singular solutions, repeated roots and completeness for higher-spin chains, Journal of Statistical Mechanics: Theory and Experiments, P03024, (2014). [arxiv]
- W. Hao, R. I. Nepomechie and A. J. Sommese, On the completeness of solutions of Bethe's equations, Physical Review E, Volume 88, 052113, (2013). [arxiv]
- W. Hao and S. Zhu, A domain decomposition finite difference scheme with third-order accuracy and unconditional stability, Applied Mathematics and Computation, Volume 219, Issue 11, pp. 6170-6181 (2013). [pdf]
- W. Hao, A. J. Sommese and Z. Zeng, Algorithm 931: An algorithm and software for computing multiplicity structures at zeros of nonlinear systems, ACM Transactions on Mathematical Software, Volume 40, Article No. 5, (2013). [pdf, MULTIPLICITY]
- W. Hao, J. D. Hauenstein, C.-W. Shu, A. J. Sommese, Z. Xu and Y.-T. Zhang, A homotopy method based on WENO schemes for solving steady state problems of hyperbolic conservation laws, Journal of Computational Physics, Volume 250, pp. 332-346 (2013). [pdf]
- W. Hao, B. Hu and A. J. Sommese, Cell cycle control and bifurcation for a free boundary problem modeling tissue growth, Journal of Scientific Computing, Volume 56, Issue 2, pp. 350-365, (2013). [pdf, Computational page]
- W. Hao, J. D. Hauenstein, B. Hu, T. McCoy and A. J. Sommese, Computing steady-state solutions for a free boundary problem modeling tumor growth by Stokes equation, Journal of Computational and Applied Mathematics, Volume 237, Issue 1, pp. 326-334, (2013). [pdf]
- W. Hao, J. D. Hauenstein, B. Hu, Y. Liu, A. J. Sommese and Y.-T. Zhang, Continuation along bifurcation branches for a tumor model with a necrotic core, Journal of Scientific Computing, Volume 53, Issue 2, pp. 395-413, (2012). [pdf]
- W. Hao, J. D. Hauenstein, B. Hu, Y. Liu, A. J. Sommese and Y.-T. Zhang, Bifurcation for a free boundary problem modeling the growth of a tumor with a necrotic core, Nonlinear Analysis Series B: Real World Applications, Volume 13, Issue 2, pp. 694-709, (2012). [pdf]
- W. Hao, J. D. Hauenstein, B. Hu and A. J. Sommese, A three-dimensional steady-state tumor system, Applied Mathematics and Computation, Volume 218, Issue 6, pp. 2661-2669, (2011). [pdf]
- W. Hao, J. D. Hauenstein, B. Hu, Y. Liu, A. J. Sommese and Y.-T. Zhang, Multiple stable steady states of a reaction-diffusion model on zebrafish dorsal-ventral patterning, Discrete and Continuous Dynamical Systems - Series S, Volume 4, Number 6, pp. 1413-1428, (2011). [pdf]
- F. Sun, M.-Q. Liu and W. Hao, An algorithmic approach to finding factorial designs with generalized minimum aberration, Journal of Complexity, Volume 25, Issue 1, pp. 75-84, (2009). [pdf]
- W. Hao and S. Zhu, Parallel iterative methods for parabolic equations, International Journal of Computer Mathematics, Volume 86, Issue 3, pp. 431-440, (2009). [pdf]
Book Chapters
- W. Hao, B. Hu and A. J. Sommese, Numerical Algebraic Geometry and Differential Equations, Future Vision and Trends on Shapes, Geometry and Algebra, (2013).