Google scholar profile

Journal publication

  1. 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).
  2. 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)
  3. 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)
  4. Y. Luo, X. Li, W. Hao, Stability Preserving Data-driven Models With Latent Dynamics , Chaos, 30(9), (2022) [arxiv]
  5. X. Zhao, W. Hao B. Hu, Two neural-network-based methods for solving elliptic obstacle problems , Chaos, Solitons & Fractals, Vol. 161, 112313,(2022)
  6. 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)
  7. 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)
  8. 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]
  9. 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]
  10. 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)
  11. Q. Chen, W. Hao, J. He, Power series expansion neural network, Journal of Computational Science, Vol. 92, pp. 1-22, (2022) [arxiv]
  12. W. Hao, C. Zheng Learn bifurcations of nonlinear parametric systems via equation driven neural networks , Chaos, 32, 011102, (2022) [arxiv]
  13. 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)
  14. W. Hao, An adaptive homotopy tracking algorithm for solving nonlinear parametric systems with applications in nonlinear ODEs, Applied Mathematics Letters, 107767, (2022)
  15. 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]
  16. 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]
  17. W. Hao, C. Zheng, A stochastic homotopy tracking algorithm for parametric systems of nonlinear equations, Journal of Scientific Computing, Vol. 87,(2021) [arxiv]
  18. 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]
  19. 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)
  20. 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)
  21. W. Hao, A gradient descent method for solving a system of nonlinear equations , Applied Mathematics Letters, Volume 112, 106739, (2021)
  22. 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]
  23. 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)
  24. 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)
  25. 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]
  26. W. Hao, C. Xue, Spatial pattern formation in reaction-diffusion models: a computational approach, Journal of Mathematical Biology, 80(1), 521-543., (2020)
  27. 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)
  28. 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]
  29. Q. Chen, W. Hao, A homotopy training algorithm for fully connected neural networks, Proceedings of the Royal Society A, 475(2231), (2019)[arxiv]
  30. 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)
  31. 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)
  32. 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]
  33. 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)
  34. A. Friedman, W. Hao, The Role of Exosomes in Pancreatic Cancer Microenvironment , Bulletin of Mathematical Biology, Vol. 80, no. 5, pp. 1111-1133. (2018).
  35. 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).
  36. 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).
  37. W. Hao, H. Komarb, P. Hart, D. Conwell, G. Lesinskid, A. Friedman Mathematical model of chronic pancreatitis , PNAS, 114 (19), 5011-5016 (2017).
  38. 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).
  39. 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).
  40. 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).
  41. A. Friedman, W. Hao, Mathematical modeling of liver fibrosis , Mathematical Biosciences and Engineering, 14(1), pp. 143--164 (2017).
  42. W. Hao, A. Friedman, Mathematical model on Alzheimer's disease , BMC Syst Biol, 10, 1:108 (2016). (Updated appendeix)
  43. 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).
  44. W. Hao, L. Schlesinger, A. Friedman, Modeling granulomas in response to infection in the lung, Plos One, 11, 3:e0148738.(2016).
  45. W. Hao, C. Marsh, A. Friedman, A Mathematical Model of Idiopathic Pulmonary Fibrosis , Plos One , 10, 9:e0135097, (2015).
  46. 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).
  47. 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).
  48. 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).
  49. 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).
  50. 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).
  51. 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]
  52. W. Hao, E. D. Crouser and A. Friedman, Mathematical model of sarcoidosis , PNAS , Vol. 111 No. 45, pp. 16065--16070, (2014).
  53. 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 )
  54. W. Hao and A. Friedman, The LDL-HDL profile determines the risk of atherosclerosis: A mathematical model, PLOS ONE, 9(3): e90497, (2014).
  55. 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]
  56. 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]
  57. 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]
  58. 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]
  59. 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]
  60. 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]
  61. 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]
  62. 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]
  63. 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]
  64. 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]
  65. 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]
  66. 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]
  67. 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

  1. W. Hao, B. Hu and A. J. Sommese, Numerical Algebraic Geometry and Differential Equations, Future Vision and Trends on Shapes, Geometry and Algebra, (2013).