Refereed Journal Articles

In Review

1. W. Dahmen, W. Li, Y. Teng, and Z. Wang. Expansive Natural Neural Gradient Flows for Energy Minimization. Under review.

2. L. Ji, S. Rashid, Y. Chen, and Z. Wang. Nonlinear Model Order Reduction on Quadratic Manifolds via Greedy Algorithms with Dimension-Dependent Regularization, under review.

3. A. Vasudevan, Z. Wang, and L. Ju. Shape Optimization for Incompressible Fluid Flows with Diffuse Domain Method, under review.

In Print

1. Z. Xu, M. Wang, and Z. Wang. Weak TransNet: A Petrov-Galerkin based neural network method for solving elliptic PDEs. Journal of Scientific Computing, Vol. 107, 2026, Article 60.

2. Y. Geng, L. Ju, B. Kramer, and Z. Wang. Data-Driven Reduced-Order Models for Port-Hamiltonian Systems with Operator Inference. Computer Methods in Applied Mechanics and Engineering, Vol. 442, 2025, Article 118042.

3. Y. Geng, J. Singh, L. Ju, B. Kramer, and Z. Wang. Gradient Preserving Operator Inference: Data-Driven Reduced-Order Models for Equations with Gradient Structure. Computer Methods in Applied Mechanics and Engineering, Vol. 427, 2024, Article 117033.

4. Y. Geng, Y. Teng, Z. Wang, and L. Ju. A deep learning method for the dynamics of classic and conservative Allen-Cahn equations based on fully-discrete operators. Journal of Computational Physics, Vol. 496, 2024, Article 112589.

5. R. Lan, L. Ju, Z. Wang, and M. Gunzburger. A second-order implicit-explicit scheme for the baroclinic-barotropic split system of primitive equations. Communications in Computational Physics, Vol. 34(5), 2023, pp. 1306–1331.

6. Y. Teng, Z. Wang, L. Ju, A. Gruber, and G. Zhang.  Level Set Learning and Function Approximation on Sparse Data through Pseudo-Reversible Neural Network. SIAM Journal on Scientific Computing, Vol. 45(3), 2023, pp. A1148–A1171.

7. A. Gruber, M. Gunzburger, L. Ju, R. Lan, and Z. Wang. Multifidelity Monte Carlo Estimation for Efficient Uncertainty Quantification in Climate-Related Modeling. Geoscientific Model Development, Vol. 16(4), 2023, pp. 1213–1229.

8. A. Gruber, M. Gunzburger, L. Ju, and Z. Wang. Energetically consistent model reduction for metriplectic systems. Computer Methods in Applied Mechanics and Engineering, Vol. 404, 2023, Article 115709.

9. A. Gruber, M. Gunzburger, L. Ju, and Z. Wang. A multifidelity Monte Carlo method for realistic computational budgets. Journal of Scientific Computing, Vol. 94, 2023, Article 2.

10. Y. Chen, L. Ji, and Z. Wang. A Hyper-Reduced MAC Scheme for the Parametric Stokes and Navier-Stokes Equations. Journal of Computational Physics, Vol. 466, 2022, Article 111412.

11. B. Koc, C. Mou, H. Liu, Z. Wang, G. Rozza, and T. Iliescu. Verifiability of the Data-Driven Variational Multiscale Reduced Order Model. Journal of Scientific Computing, Vol. 93, 2022, Article 54.

12. W. Dahmen, M. Wang, and Z. Wang. Nonlinear Reduced DNN Models for State Estimation. Communications in Computational Physics, Vol. 32(1), 2022, pp. 1–40.

13. W. Hu, J. Liu, and Z. Wang. Bilinear Control of Convection-Cooling: From Open-Loop to Closed-Loop. Applied Mathematics and Optimization, Vol. 86, 2022, Article 5.

14. R. Lan, L. Ju, Z. Wang, M. Gunzburger, and P. Jones. High-Order Multirate Explicit Time-Stepping Schemes for the Baroclinic-Barotropic Split Dynamics in Primitive Equations. Journal of Computational Physics, Vol. 457, 2022, Article 111050.

15. A. Gruber, M. Gunzburger, L. Ju, and Z. Wang. A Comparison of Neural Network Architectures for Data-Driven Reduced-Order Modeling. Computer Methods in Applied Mechanics and Engineering, Vol. 393, 2022, Article 114764.

16. X. Feng, Y. Luo, L. Vo, and Z. Wang. An Efficient Iterative Method for Solving Parameter-Dependent and Random Diffusion Problems. Journal of Scientific Computing, Vol. 90, 2022, Article 72.

17. H. Sharma, Z. Wang, and B. Kramer. Hamiltonian Operator Inference: Physics-preserving Learning of Reduced-Order Models for Hamiltonian Systems. Physica D: Nonlinear Phenomena, Vol. 431, 2022, 133122.

18. J. Liu and Z. Wang. A ROM-accelerated Parallel-in-time Preconditioner for Solving All-at-once Systems from Evolutionary PDEs. Applied Mathematics and Computation, Vol. 416, 2021, 126750.

19. L. Feng, G. Fu, and Z. Wang. A FOM/ROM Hybrid Approach for Accelerating Numerical Simulations. Journal of Scientific Computing, Vol. 89, 2021, Article 61.

20. R. Lan, W. Leng, Z. Wang, L. Ju, and M. Gunzburger. Parallel Exponential Time Differencing Methods for Geophysical Flow Simulations. Computer Methods in Applied Mechanics and Engineering, Vol. 387, 2021, 114151.

21. C. Mou, Z. Wang, D. Wells, X. Xie, and T. Iliescu. Reduced Order Models for the Quasi-Geostrophic Equations: A Brief Survey. Fluids, Vol. 6(1), 2021, 16.

22. X. Meng, T. Hoang, Z. Wang, and L. Ju. Localized exponential time differencing methods for shallow water equations: algorithms and numerical study. Communications in Computational Physics, Vol. 29(1), 2021, pp. 80–110.

23. A. Gruber, M. Gunzburger, L. Ju, Y. Teng, and Z. Wang. Nonlinear Level Set Learning for Function Approximation on Sparse Data with Applications to Parametric Differential Equations. Numerical Mathematics: Theory, Methods and Applications, Vol. 14(4), 2021, pp. 839–861.

24. G. Fu and Z. Wang. POD-(H)DG method for incompressible flow simulations. Journal of Scientific Computing, Vol. 85, 2020, Article 24.

25. L. Ju, W. Leng, Z. Wang, and S. Yuan. Numerical investigation of ensemble methods with block iterative solvers for evolution problems. Discrete and Continuous Dynamical Systems, Series B, Vol. 25(12), 2020, pp. 4905–4923.

26. T. Hoang, L. Ju, and Z. Wang. Nonoverlapping localized Exponential Time Differencing methods for diffusion problems. Journal of Scientific Computing, Vol. 82, 2020, Article 37.

27. T. Hoang, L. Ju, W. Leng, and Z. Wang. High order explicit local time-stepping methods for hyperbolic conservation laws. Mathematics of Computation, Vol. 89, 2020, pp. 1807–1842.

28. M. Gunzburger, N. Jiang, and Z. Wang. An efficient algorithm for simulating ensembles of parameterized flow problems. IMA Journal of Numerical Analysis, Vol. 39(3), 2019, pp. 1180–1205.

29. M. Gunzburger, N. Jiang, and Z. Wang. A second-order time-stepping scheme for simulating ensembles of parameterized flow problems. Computers and Mathematics with Applications, Vol. 19(3), 2019, pp. 681–701.

30. J. Liu and Z. Wang. Non-commutative discretize-then-optimize algorithms for elliptic PDE-constrained optimal control problems. Journal of Computational and Applied Mathematics, Vol. 362, 2019, pp. 596–613.

31. T. Hoang, W. Leng, L. Ju, Z. Wang, and K. Pieper. Conservative explicit local time-stepping schemes for the shallow water equations. Journal of Computational Physics, Vol. 382, 2019, pp. 152–176.

32. Y. Luo and Z. Wang. A Multilevel Monte Carlo Ensemble Scheme for Solving Random Parabolic PDEs. SIAM Journal on Scientific Computing, Vol. 41(1), 2019, pp. A622–A642.

33. Y. Luo and Z. Wang. An ensemble algorithm for numerical solutions to deterministic and random parabolic PDEs. SIAM Journal on Numerical Analysis, Vol. 56(2), 2018, pp. 859–876.

34. T. Hoang, L. Ju, and Z. Wang. Overlapping localized exponential time differencing methods for diffusion problems. Communications in Mathematical Sciences, Vol. 16(6), 2018, pp. 1531–1555.

35. J. Liu and Z. Wang. Efficient time domain decomposition algorithms for parabolic PDE-constrained optimization problems. Computers and Mathematics with Applications, Vol. 75(6), 2018, pp. 2115–2133.

36. H. Fu, H. Wang, and Z. Wang. POD/DEIM Reduced-Order Modeling of Time-Fractional Partial Differential Equations with Applications in Parameter Identification. Journal of Scientific Computing, Vol. 74(1), 2018, pp. 220–243.

37. X. Xie, D. Wells, Z. Wang, and T. Iliescu. Numerical analysis of the Leray reduced order model. Journal of Computational and Applied Mathematics, Vol. 328, 2018, pp. 12–29.

38. B. Cockburn and Z. Wang. Adjoint-based, superconvergent Galerkin approximations of linear functionals. Journal of Scientific Computing, Vol. 73(2–3), 2017, pp. 644–666.

39. L. Ju and Z. Wang. Exponential Time Differencing Gauge Method for Incompressible Viscous Flows. Communications in Computational Physics, Vol. 22, 2017, pp. 517–541.

40. D. Wells, Z. Wang, X. Xie, and T. Iliescu. An Evolve-Then-Filter Regularized Reduced Order Model for Convection-Dominated Flows. International Journal for Numerical Methods in Fluids, Vol. 84, 2017, pp. 598–615.

41. Y. Gong, Q. Wang, and Z. Wang. Structure-Preserving Galerkin POD Reduced-Order Modeling of Hamiltonian Systems. Computer Methods in Applied Mechanics and Engineering, Vol. 315, 2017, pp. 780–798.

42. X. Xie, D. Wells, Z. Wang, and T. Iliescu. Approximate Deconvolution Reduced Order Modeling. Computer Methods in Applied Mechanics and Engineering, Vol. 313, 2017, pp. 512–534.

43. J. Borggaard, Z. Wang, and L. Zietsman. A Goal-Oriented Model Reduction Approach for Complex Systems. Computers and Mathematics with Applications, Vol. 71(11), 2016, pp. 2155–2169.

44. Z. Wang, B. McBee, and T. Iliescu. Approximate Partitioned Methods of Snapshots for POD. Journal of Computational and Applied Mathematics, Vol. 307, 2016, pp. 374–384.

45. L. Rondi, F. Santosa, and Z. Wang. A Variational Approach to the Inverse Photolithography Problem. SIAM Journal on Applied Mathematics, Vol. 76(1), 2016, pp. 110–137.

46. Z. Wang. Nonlinear Model Reduction Based on the Finite Element Method With Interpolated Coefficients: Semilinear Parabolic Equations. Numerical Methods for Partial Differential Equations, Vol. 31(6), 2015, pp. 1713–1741.

47. T. Iliescu and Z. Wang. Are the Snapshot Difference Quotients Needed in the Proper Orthogonal Decomposition? SIAM Journal on Scientific Computing, Vol. 36(3), 2014, pp. A1221–A1250.

48. T. Iliescu and Z. Wang. Variational Multiscale Proper Orthogonal Decomposition: Navier-Stokes Equations. Numerical Methods for Partial Differential Equations, Vol. 30, 2014, pp. 641–663.

49. T. Iliescu and Z. Wang. Variational Multiscale Proper Orthogonal Decomposition: Convection-Dominated Convection-Diffusion-Reaction Equations. Mathematics of Computation, Vol. 82, 2013, pp. 1357–1378.

50. E. Foster, T. Iliescu, and Z. Wang. A Finite Element Discretization of the Streamfunction Formulation of the Stationary Quasi-Geostrophic Equations of the Ocean. Computer Methods in Applied Mechanics and Engineering, Vol. 261–262, 2013, pp. 105–117.

51. J. Huang, Z. Wang, and R. Zhu. Asymptotic Error Expansions for Hypersingular Integrals. Advances in Computational Mathematics, Vol. 38(2), 2013, pp. 257–279.

52. Z. Wang, I. Akhtar, J. Borggaard, and T. Iliescu. Proper Orthogonal Decomposition Closure Models for Turbulent Flows: A Numerical Comparison. Computer Methods in Applied Mechanics and Engineering, Vol. 237–240, 2012, pp. 10–26.

53. I. Akhtar, Z. Wang, J. Borggaard, and T. Iliescu. A New Closure Strategy for Proper Orthogonal Decomposition Reduced-Order Models. Journal of Computational and Nonlinear Dynamics, Vol. 7(3), 2012, 034503.

54. O. Roderick, M. Anitescu, and Z. Wang. Reduced Order Approximations in Uncertainty Analysis of Nuclear Engineering Applications. Transactions of the American Nuclear Society, Vol. 106, 2012.

55. W. Feng, X. He, Z. Wang, and X. Zhang. Non-Iterative Domain Decomposition Methods for a Non-Stationary Stokes-Darcy Model with Beavers-Joseph Interface Condition. Applied Mathematics and Computation, Vol. 219(2), 2012, pp. 453–463.

56. P. Cheng, J. Huang, and Z. Wang. Nystrom Methods and Extrapolation for Solving Steklov Eigensolutions and its Application in Elasticity. Numerical Methods for Partial Differential Equations, Vol. 28(6), 2012, pp. 2021–2040.

57. P. Cheng, X. Luo, Z. Wang, and J. Huang. Mechanical Quadrature Methods and Extrapolation Algorithms for Boundary Integral Equations with Linear Boundary Conditions in Elasticity. Journal of Elasticity, Vol. 108(2), 2012, pp. 193–207.

58. Z. Wang, I. Akhtar, J. Borggaard, and T. Iliescu. Two-Level Discretizations of Nonlinear Closure Models for Proper Orthogonal Decomposition. Journal of Computational Physics, Vol. 230(1), 2011, pp. 126–146.

59. J. Borggaard, T. Iliescu, and Z. Wang. Artificial Viscosity Proper Orthogonal Decomposition. Mathematical and Computer Modelling, Vol. 53(1–2), 2011, pp. 269–279.

60. O. Roderick, Z. Wang, and M. Anitescu. Dimensionality Reduction for Uncertainty Quantification of Nuclear Engineering Models. Transactions of the American Nuclear Society, Vol. 104, 2011.

61. O. San, A. E. Staples, Z. Wang, and T. Iliescu. Approximate Deconvolution Large Eddy Simulation of a Barotropic Ocean Circulation Model. Ocean Modelling, Vol. 40, 2011, pp. 120–132.

62. P. Cheng, J. Huang, and Z. Wang. Mechanical Quadrature Methods and Extrapolation for Solving Nonlinear Boundary Helmholtz Integral Equations. Applied Mathematics and Mechanics (English Edition), Vol. 32(12), 2011, pp. 1505–1514.

63. B. Hu and Z. Wang. Combined Hybrid Method Applied in the Reissner-Mindlin Plate Model. Finite Elements in Analysis and Design, Vol. 46(5), 2010, pp. 428–437.

64. J. Huang and Z. Wang. Extrapolation Algorithms for Solving Mixed Boundary Integral Equations of the Helmholtz Equation by Mechanical Quadrature Methods. SIAM Journal on Scientific Computing, Vol. 31(6), 2009, pp. 4115–4129.

65. Z. Wang and B. Hu. Research of Combined Hybrid Method Applied in the Reissner-Mindlin Plate Model. Applied Mathematics and Computation, Vol. 182(1), 2006, pp. 49–66.

Selected Papers in Chinese

1. J. Liu, B. Hu, Y. Xu, and Z. Wang. A semi-discrete mixed finite element method for the Sobolev equation. Sichuan Daxue Xuebao, Vol. 46(2), 2009, pp. 297–301.

2. B. Hu, Z. Wang, and Y. Xu. Improvement of the Selective Reduced Integration Element S1 for the Reissner-Mindlin Plate. Sichuan Daxue Xuebao, Vol. 43(1), 2006, pp. 47–51.

3. Y. Zhang, B. Hu, and Z. Wang. Combined Hybrid Finite Element Methods for the Poisson Equation. Sichuan Daxue Xuebao, Vol. 42(3), 2005, pp. 467–470.

4. Y. Wu, J. Zhou, Z. Wang, and Y. Zeng. Parameter Estimation of Weibull Distribution Using the EM Algorithm Based on Randomly Censored Data. Sichuan Daxue Xuebao, Vol. 42(5), 2005, pp. 910–913.

Refereed Proceedings

1. Y. Teng, X. Zhang, Z. Wang, and L. Ju. Learning Green’s Functions of Linear Reaction-Diffusion Equations with Application to Fast Numerical Solver. Proceedings of Machine Learning Research, 3rd Annual Conference on Mathematical and Scientific Machine Learning, 2022.

2. I. Akhtar, Z. Wang, J. Borggaard, and T. Iliescu. A Novel Strategy for Nonlinear Closure in Proper Orthogonal Decomposition Reduced-Order Models. ASME ECTC, October 1–2, 2010.

3. I. Akhtar, Z. Wang, J. Borggaard, and T. Iliescu. Large Eddy Simulation Ideas for Nonlinear Closure in Model Reduction of Fluid Flows. AIAA 2010-5089.

4. I. Akhtar, J. Borggaard, T. Iliescu, and Z. Wang. Closure for Improved Reduced-Order Models using High Performance Computing. AIAA 2010-1276.

5. J. Borggaard, A. Duggleby, A. Hay, T. Iliescu, and Z. Wang. Reduced-order Modeling of Turbulent Flows. In Proceedings of MTNS, 2008.

Dissertation

Z. Wang. Reduced-Order Modeling of Complex Engineering and Geophysical Flows: Analysis and Computations. Ph.D. Thesis, Virginia Tech, 2012.