Research Interests

  • Numerical PDEs and stiff ODEs

  • Inverse problems and PDE-constrained optimization

  • High performance computing and parallel algorithm

  • Deep learning and applications in solving PDEs

    Research Grants

  • Mitacs Accelerate Grant (PI), $45,000, 2019 - 2020

  • NSERC Collaborative Research and Development Grant (PI), $144,000, 2019- 2021

  • NSERC Individual Discovery Grant (PI), $85,000, 2019-2024

  • Mitacs Elevate Grant (PI), $110,000, 2016 - 2018

  • PIMS workshop grant (CO-PI), "Geophysical and Imaging and Inversion", $10,000, 2017

  • NSERC Individual Discovery Grant (PI), $55,000, 2014 - 2019

  • NSERC Engage Plus Grant (PI), $ 27,650, 2014 - 2014

  • NSERC Engage Grant (PI), $ 25,000, 2013 - 2014

  • PIMS workshop grant (PI), $10,000, "Recent Developments of Numerical methods for Seismic Inverse Problems and Applications ", 2013

  • NSERC Individual Discovery Grant (PI), $ 86,500, 2008 - 2013

  • NSERC Research Tools and Infrastructure(Co-PI), $ 46,910, 2010

  • MITACS Accelerate grant (PI) , $ 15,000, 2008

  • University of Calgary Startup Fund (PI), $ 31,000, 2007 - 2009

    Publications

      Submitted:

    1. Da Li, Michael P. Lamoureux, and Wenyuan Liao, Full waveform inversion with unbalanced optimal transport distance, Journal of Computational Physics, submitted.

    2. Da Li, Keran Li, and Wenyuan Liao, Efficient and Stable Finite Difference Modelling of Acoustic Wave Propagation in Variable-density Media, Computers and Mathematics with Applications, submitted, also available arXiv preprint arXiv:2003.09812.

    3. Hatef Dastour, Wenyuan Liao, A generalized optimal fourth-order finite difference scheme for a 2D Helmholtz equation with the perfectly matched layer boundary condition, Journal of Computational and Applied Mathematics, Under Review.

    4. J. Huang, W. Liao, T. Xin, F. Xie, H. Yu and P. Yong, A source-independent waveform inversion method based on the similarity of seismic data, Journal of Geophysics and Engineering, submitted.

      Published/Accepted:

    5. Hatef Dastour, Wenyuan Liao, An optimal 13-point finite difference scheme for a 2D Helmholtz equation with a perfectly matched layer boundary condition, accepted, to appear in Numerical Algorithms.

    6. Keran Li, Wenyuan Liao, An efficient and high accuracy finite-difference scheme for the acoustic wave equation in 3D heterogeneous media, Journal of Computational Science, 40(2020),101063.

    7. Yong, Peng, Jianping Huang, Zhenchun Li, Wenyuan Liao, and Luping Qu. Least-squares reverse time migration via linearized waveform inversion using a Wasserstein metric. Geophysics, 84, no. 5 (2019): 1-88.

    8. Xiong, Zhi, Qingrun Zhang, Alexander Platt, Wenyuan Liao, Xinghua Shi, Gustavo de los Campos, and Quan Long. OCMA: Fast, Memory-Efficient Factorization of Prohibitively Large Relationship Matrices. G3: Genes, Genomes, Genetics, 9, no. 1 (2019): 13-19.

    9. Li, Keran, Wenyuan Liao, and Yaoting Lin. A compact high order Alternating Direction Implicit method for three-dimensional acoustic wave equation with variable coefficient. Journal of Computational and Applied Mathematics, 361 (2019): 113-129.

    10. Dastour, Hatef, and Wenyuan Liao. A fourth-order optimal finite difference scheme for the Helmholtz equation with PML. Computers & Mathematics with Applications, 78, no. 6 (2019): 2147-2165.

    11. Yong, Peng, Wenyuan Liao, Jianping Huang, Zhenchun Li, and Yaoting Lin. Misfit function for full waveform inversion based on the Wasserstein metric with dynamic formulation. Journal of Computational Physics, 399 (2019): 108911.

    12. Yong, P., Huang, J., Li, Z., Liao, W. (2018, June). Earth Mover's Distance Based On Gradient Flow for Full Waveform Inversion. In 80th EAGE Conference and Exhibition, 2018.

    13. Yong, P., Liao, W., Huang, J., Li, Z. (2018). Total variation regularization for seismic waveform inversion using an adaptive primal dual hybrid gradient method. Inverse Problems, 34(4), p.045006.

    14. Ghaderpour, Ebrahim, Wenyuan Liao, and Michael P. Lamoureux. Antileakage least-squares spectral analysis for seismic data regularization and random noise attenuation. Geophysics, 83, no. 3 (2018): V157-V170.

    15. Huang, Jianping, Wenyuan Liao, and Zhenchun Li. A multi-block finite difference method for seismic wave equation in auxiliary coordinate system with irregular fluid–solid interface. Engineering Computations, 35.1 (2018): 334-362.

    16. Lin, Yaoting, Wei Zhou, and Wenyuan Liao. A Bayesian Approach for Seismic Inversion at Roncott Research Area. In 2018 International Conference on Mathematics, Modelling, Simulation and Algorithms (MMSA 2018). Atlantis Press, 2018.

    17. W. Liao, P. Yong, H. Dastour and J. Huang, Efficient and accurate numerical simulation of acoustic wave propagation in a 2D heterogeneous media, Applied Mathematics and Computation, 321,(2018); pp 385-400.

    18. Liao, Wenyuan, and Ou Wei. A Fourth-Order Compact Numerical Scheme for Three-Dimensional Acoustic Wave Equation with Variable Velocity. In International Conference on Applied Mathematics, Modeling and Computational Science, pp. 279-289. Springer, Cham, 2017. Wei, O., Guo, Z., Niu, Y., Liao, W. (2017). Model checking optimal finite-horizon control for probabilistic gene regulatory networks. BMC Systems Biology, 11(6):104, pp 75-88.

    19. C. Cui, JP Huang, Z. Li, W. Liao and Z. Guan, Reflection full-waveform inversion using a modified phase misfit function, Applied Geophysics, 14(3), 407 - 418, 2017.

    20. Chen, Yan, Xuhong Tian, Hui Liu, Zhangxin Chen, Bo Yang, Wenyuan Liao, Peng Zhang, Ruijian He, and Min Yang. Parallel ILU preconditioners in GPU computation, Soft Computing, (2017): 1-19.

    21. P. Yong, J. Huang, Z. Li, W. Liao, L. Qu, Q. Li, P. Liu, Optimized equivalent staggered-grid FD method for elastic wave modelling based on plane wave solutions. Geophysical Journal International, 208.2 (2017): 1157-1172.

    22. M. Yuan, J. Huang, W. Liao, F. Jiang, Least-squares Gaussian beam migration. Journal of Geophysics and Engineering, 14.1 (2017): 184.

    23. E. Ghaderpour, W. Liao, M. Lamoureux, D. Li, S. Pagiatakis, Anti-leakage least-squares spectral analysis for data regularization, GeoConvention 2017 conference proceeding, May 2017.

    24. W. Pan, K. Innanen and W. Liao, Accelerating Hessian-free Gauss-Newton full-waveform inversion via L-BFGS preconditioned conjugate-gradient algorithm, GEOPHYSICS, 82, 2(2017); pp. R49-R64.

    25. Wei, O., Guo, Z., Niu, Y., Liao, W. (2016, December). Optimal control for context-sensitive probabilistic Boolean networks with perturbation using probabilisitic model checking. IEEE proceeding, 2016 IEEE International Conf. on Bioinformatics and Biomedicine. (pp. 210-216). IEEE.

    26. Yong, P., Huang, J., Li, Z., Liao, W., Qu, L., Li, Q., Yuan, M. (2016). Elastic-wave reverse-time migration based on decoupled elastic-wave equations and inner-product imaging condition. Journal of Geophysics and Engineering, 13(6), 953.

    27. Guo, John, Ye Zheng, and Wenyuan Liao. High Fidelity Seismic Trace Interpolation. 2015 SEG Annual Meeting. Proceeding of Society of Exploration Geophysicists, 2015.

    28. Liao, Wenyuan. An adjoint-based Jacobi-type iterative method for elastic full waveform inversion problem. Applied Mathematics and Computation, 267 (2015): 56-70.

    29. Zheng, Y., Guo, J., Liao, W., Ross, L., Nemeth, B., Escalante, C. (2015, December). Choice of Algorithm and Data Domain for 5D Trace Interpolation. In 2015 SEG Annual Meeting. Proceeding of Society of Exploration Geophysicists

    30. Huang, J., Yang, J., Liao, W., Wang, X., Li, Z. (2015). Common - shot Fresnel beam migration based on wave-field approximation in effective vicinity under complex topographic conditions. Geophysical Prospecting, 2015 Aug.

    31. Huang, J., Yuan, M., Liao, W., Li, Z., Yue, Y. (2015). Accurate acoustic and elastic beam migration without slant stack for complex topography. Journal of Geophysics and Engineering, 12(3), 515.

    32. Cao, Danping, and Wenyuan Liao. A computational method for full waveform inversion of crosswell seismic data using automatic differentiation. Computer Physics Communications, 188 (2015): 47-58.

    33. Guo, John, Ye Zheng, and Wenyuan Liao. Arbitrarily Sampled Fourier Transform for 5D Interpolation. Proceeding of GeoConvention 2015, Canadian Society of Exploration Geophysicists (CSEG)).

    34. W. Liao, A Strongly A-Stable Time Integration Method for Solving the Nonlinear Reaction-Diffusion Equation, Abstract and Applied Analysis, Vol. 2015(2015), Article ID 539652, 12 pages, http://dx.doi.org/10.1155/2015/539652.

    35. W. Liao, On the dispersion, stability and accuracy of a compact higher-order finite difference scheme for 3D acoustic wave equation, Journal of Computational and Applied Mathematics, Vol. 270 (2014),571-583.

    36. S. Das, W. Liao and A. Gupta, An efficient fourth-order low dispersive finite difference scheme for 2-D acoustic wave equation, Journal of Computational and Applied Mathematics, Vol. 258 (2014), 151-167.

    37. D. Cao, W. Liao, An Adjoint-Based Hybrid Computational Method for Crosswell Seismic Inversion, Computing in Science and Engineering, Vol. 16(6), Nov. 2014.

    38. W. Liao and D. Cao, Compact fourth-order finite-difference modeling for 3D acoustic wave equation, SEG Extended Abstract, 2013.

    39. W. Liao, High-order ADI finite difference scheme for 3D reaction-diffusion equation with Neumann boundary condition. Numerical Methods for Partial Differential Equations, vol. 29, issue 3, pp. 778 - 798(May, 2013).

    40. D. Cao and W. Liao, Full waveform inversion of crosswell seismic data using automatic differentiation, GeoConvention 2013: Integration, CSEG Extended Abstract

    41. W. Liao, A compact higher-order finite difference method for solving the unsteady convection-diffusion equation, International Journal for Computational Methods in Engineering Science & Mechanics , vol. 13, 3, pp. 135 - 145 (2012).

    42. W. Liao, A computational method to estimate the unknown coefficient in a wave equation using boundary measurements, Inverse Problems in Science & Engineering , vol. 19, issue 6, pp. 855 - 877, (2011).

    43. W. Liao, A numerical method to identify the acoustic coefficients in a two-dimensional wave equation, Proceedings of the 4th IEEE International Conference on Computer Science and Information Technology, Vol. 4, pp. 395 - 399, 2011.

    44. W. Liao and Y. Yan, Singly Diagonally Implicit Runge-Kutta Method for Time-Dependent Reaction-Diffusion Equation, Numerical Methods for Partial Differential Equations , vol. 27, 6, pp. 1423 - 1441, (2011).

    45. W. Liao and J. Zhu, Efficient and accurate finite difference schemes for solving one-dimensional Burgers' equation, International Journal of Computer Mathematics. vol. 88, 12, pp. 2575-2590 (2011)

    46. W. Liao, A fourth-order finite difference method for solving the system of two-dimensional Burgers' equations, International Journal for Numerical Methods in Fluids Volume 64, Issue 5, 2010, Pages 565 - 590.

    47. O. Volkov, B. Protas, W. Liao and D. Glander, Adjoint-based optimization of thermo-fluid phenomena in welding processes, Journal of Engineering Mathematics.Volume 65, Number 3, November 2009, Pages 201 - 220.

    48. W. Liao, M. Dehghan and A. Mohebbi, Direct numerical method for an inverse problem of a parabolic partial differential equation, Journal of Computational and Applied Mathematics, Volume 232, Issue 2, 15 October 2009, Pages 351-360.

    49. W. Liao and Abdul Q. M. Khaliq, High-order compact scheme for solving nonlinear Black-Scholes equations with transaction cost, International Journal of Computer Mathematics, vol. 86, 6, 2009, pp. 1009-1023.

    50. W. Liao and J. Zhu, An accurate and efficient numerical method for solving Black-Scholes equation in option pricing, International Journal of Mathematics in operational Research, vol. 1, 1, 2009, pp. 191-210.

    51. W. Liao, An implicit fourth-order compact finite difference scheme for one-dimensional Burgers' equation, Applied Mathematics and Computation, vol 206, 2(December 2008), pp. 755-764.

    52. W. Liao and J. Zhu, A new method for solving convection-diffusion equations, Proceedings of the 11th IEEE International Conference on Computational Science and Engineering, pp. 107 - 114, IEEE Computer Society, 2008.

    53. B. Protas and W. Liao, Adjoint-based optimization of PDEs in moving domains, Journal of Computational Physics, vol 227, 4 (Feburary, 2008), pp. 2707-2723.

    54. Liao, Wenyuan, and Abdul QM Khaliq. High Order Compact Finite Difference Scheme for Solving Nonlinear Black-Scholes equation with Transaction Costs. Computational and Mathematical Methods in Science and Engineering, (2007) 261-271.

    55. W. Liao, A. Sandu, G.R. Carmichael, and T. Chai, Total Energy Singular Vector Analysis for Atmospheric Chemical Transport Models, Monthly Weather Review, Vol. 134, No. 9, p.2443-2465, 2006.

    56. W. Liao, J. Zhu and A.Q.M. Khaliq, A fourth-order compact algorithm for nonlinear reaction-diffusion equations with Neumann boundary conditions, Numerical Methods for Partial Differential Equations, Volume 22, Issue 3, Date: May 2006, Pages: 600-616.

    57. A. Sandu, W. Liao, G.R. Carmichael, D.K. Henze, and J.H. Seinfeld, Inverse Modeling of Aerosol Dynamics using Adjoints - Theoretical and Numerical Considerations, Aerosol Science and Technology, Vol. 39 Issue 8, p677-694, Aug. 2005.

    58. A. Sandu, E.M. Constantinescu, W. Liao, G.R. Carmichael, T. Chai, J.H. Seinfeld, and D. Duaescu, Ensemble-Based Data Assimilation for Atmospheric Chemical Transport Models, Lecture Notes in Computer Science, Vol. 3515, p. 648-655, Springer-Verlag GmbH, 2005.

    59. Emil M. Constantinescu, Wenyuan Liao, and Adrian Sandu, Mesh refinement strategies in air quality modeling, High Performance Computing Symposium, 2005, pages 158-163, San Diego, CA.

    60. E.M. Constantinescu, W. Liao, and A. Sandu, On Adaptive Mesh Refinement in High Resolution Air Quality Modeling, Lecture Notes in Computer Science, Vol. 3515, p. 798-805, Springer-Verlag GmbH, 2005.

    61. W. Liao and A. Sandu, Total Energy Singular Vectors for Atmospheric Chemical Transport Models, Lecture Notes in Computer Science, Vol. 3515, p. 806-813, Springer-Verlag GmbH, 2005.

    62. D.K. Henze, J.H. Seinfeld, W. Liao, A. Sandu, G.R. Carmichael, Inverse Modeling of Aerosol Dynamics: Condensational Growth, Journal of Geophysical Research, Vol. 109, D14201, doi:10.1029/2004JD004593, 14 pages, July 2004.

    63. A. Sandu, W. Liao, G.R. Carmichael, D. Henze, J.H. Seinfeld, T. Chai, and D. Daescu, Computational Aspects of Data Assimilation for Aerosol Dynamics, Lecture Notes in Computer Science, Springer-Verlag GmbH, Vol. 3038, p. 709-716, 2004.

    64. Y. Gu, W. Liao and J. Zhu, An efficient high-order algorithm for solving systems of 3-D reaction-diffusion equations, Journal of Computational and Applied Mathematics, Volume 155, Issue 1, 1 June 2003, Pages 1-17.

    65. W. Liao, J. Zhu and A.Q.M. Khaliq, An efficient high-order algorithm for solving systems of reaction-diffusion equations, Numerical Methods for Partial Differential Equations, Volume 18 Issue 3, 2002, Pages 340-354.

    66. W. Liao and Q. Li, A class of semi-implicit multistep Runge-Kutta methods for stiff ODEs, Journal of Tsinghua University, 39 (1999), no. 6, 1-6.

    67. W. Liao and Q. Li, A class of multistep interpolation methods for solving stiff ordinary differential equations and parallel implementation, Journal on Numerical Methods and Computer Applications, 20 (1999), no. 2, 98-106.

    68. W. Liao and Q. Li, Implementation of parallel diagonal implicit Runge-Kutta algorithms of multistep Runge-Kutta methods, Journal on Numerical Methods and Computer Applications, 20 (1999), no. 1, 70-80.

    69. W. Liao and Q. Li, A class of mixed type methods for solving stiff ODEs and the parallel implementation, Tsinghua Science and Technology, 3 (1998), no. 4, 1221-1226,1232.