Numerical PDEs and stiff ODEs
Inverse problems and PDE-constrained optimization
High performance computing and parallel algorithm
Deep learning and applications in solving PDEs
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
- Da Li, Michael P. Lamoureux, and Wenyuan Liao, Full waveform inversion with unbalanced optimal transport distance,
Journal of Computational Physics, submitted.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- Huang, Jianping, Wenyuan Liao, and Zhenchun Li. A multi-block finite difference method for seismic wave equation in auxiliary coordinate system with irregular fluidâ€“solid interface. Engineering Computations, 35.1 (2018): 334-362.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- M. Yuan, J. Huang, W. Liao, F. Jiang, Least-squares Gaussian beam migration. Journal of Geophysics and Engineering, 14.1 (2017): 184.
- 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.
- 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.
- 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.
- 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.
- Guo, John, Ye Zheng, and Wenyuan Liao. High Fidelity Seismic Trace Interpolation. 2015 SEG Annual Meeting. Proceeding of Society of Exploration Geophysicists, 2015.
- Liao, Wenyuan. An adjoint-based Jacobi-type iterative method for elastic full waveform inversion problem. Applied Mathematics and Computation, 267 (2015): 56-70.
- 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
- 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.
- 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.
- 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.
- Guo, John, Ye Zheng, and Wenyuan Liao. Arbitrarily Sampled Fourier Transform for 5D Interpolation.
Proceeding of GeoConvention 2015, Canadian Society of Exploration Geophysicists (CSEG)).
- 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.
- 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.
- 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.
- D. Cao, W. Liao, An Adjoint-Based Hybrid Computational Method for Crosswell Seismic Inversion,
Computing in Science and Engineering, Vol. 16(6), Nov. 2014.
- W. Liao and D. Cao, Compact fourth-order finite-difference modeling for 3D acoustic wave equation, SEG Extended Abstract, 2013.
- 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).
- D. Cao and W. Liao, Full waveform inversion of crosswell seismic data using automatic differentiation, GeoConvention 2013: Integration,
CSEG Extended Abstract
- 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).
- 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).
- 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.
- 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).
- 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)
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.