Ming-Chih Lai

My CV

Education:

Ph.D in Mathematics, September 1998, Courant Institute of Mathematical Sciences, New York University
Thesis: Simulations of the Flow Past an Array of Circular Cylinders as a Test of the Immersed Boundary Method.
Thesis Advisor: Charles S. Peskin
M.S in Applied Math., NTHU, Taiwan
B.S in Applied Math., NCHU, Taiwan

Research Interests:

Machine Learning for PDEs
Numerical methods for PDEs
Computational fluid mechanics

Positions:

2021/08-- Dean of College of Science, National Yang Ming Chiao Tung University
2021/02-- Lifetime Chair Professor, National Yang Ming Chiao Tung University
2014/12-- 2020/12 Chair Professor, National Chiao Tung University
2019/08-- Joint Appointment Professor, AI College, NCTU
2013/08-- Joint Appointment Research Fellow, Academia Sinica
2011/06-- 2014/11 Distinguished Professor, National Chiao Tung University
2013/01-- 2013/05 Visiting Professor, Hong Kong Baptist University
2012/09-- 2012/12 Visiting Professor, Research Institute for Mathematical Sciences (RIMS), Kyoto University
2009/08-- 2012/07 Founding Director, Center of Mathematical Modeling and Scientific Computing (CMMSC), National Chiao Tung University
2007/08-- 2009/07 Chair, Department of Applied Mathematics, National Chiao Tung University
2005/08-- Professor, Department of Applied Mathematics, National Chiao Tung University
2002/08-- 2005/07, Associate Professor, Department of Applied Mathematics, National Chiao Tung University
1999/08-- 2002/07, Assistant Professor, Department of Mathematics, National Chung Cheng University
1998/08-- 1999/07, Research Associate, Duke University

Prizes and Awards:

TWSIAM Fellow, 2021
Outstanding Alumnus, National Chung Hsing University, 2018
Ministry of Education, National Chair Professorship, 2017
Ministry of Education, Academic Award, 2014
National Science Council, Outstanding Research Award, 2011
Mathematical Society of ROC, Academic Award, 2011
National Science Council, Outstanding Scholar Research Grant, 2009/08-2012/07
National Chiao Tung University, Academic Research Award, 2005
National Science Council, Outstanding Research Award, 2003
Dean's Special Recognition Award, 2003
Kurt O. Friedrichs Prize for an outstanding dissertation in Mathematics, 1999

Scientific Committees:

Taiwan Society for Industrial and Applied Mathematics (TWSIAM), President, 2018/06- 2020/05
Mathematical Society of ROC (Taiwan), President, 2016-2017
National Center for Theoretical Sciences (NCTS), Math Division, Deputy Director, 2016-2020
SIAM Membership committee, 2014-2016
SIAM East Asia Section (EASIAM), President, 2013-2014
National Science Council, Mathematics Division, Grant panel chair 2012-2014
SIAM East Asia Section (EASIAM), Vice President, 2011-2012
National Science Council, Mathematics Division , Grant panel 2009-2011
National Center for Theoretical Sciences (NCTS), Program committee 2005-2011, Executive Committee 2012-

Editorial Boards:

Communications in Computational Physics (IF=3.791), 2012 -
East Asian Journal on Applied Mathematics (IF=1.660), 2010 -
Taiwanese Journal of Mathematics, 2014/08 - 2017/07
Journal of Biological Systems, 2013 - 2015
Advances in Applied Mathematics and Mechanics, 2009 -2018/04

Publication list:
  1. C.-C. Chang ,C.-Y. Dai, W.-F. Hu, T.-S. Lin, and M.-C. Lai, A hybrid neural-network and MAC scheme for Stokes interface problems, submitted for publication. arXiv:2306.06333v2
  2. M.-C. Lai, Y. Song, X. Yuan, H. Yue, T. Zeng, The hard-constraint PINNs for interface optimal control problems, submitted for publication. arXiv:2308.06709v1
  3. W.-F. Hu, T.-S. Lin, M.-C. Lai, Multiple discontinuous function approximations by single continuous network architecture and applications, submitted for publication.
  4. C. Wang, M.-C. Lai, Z. Zhang, An improved phase-field algorithm for simulating the impact of a drop on a substrate in the presence of surfactants, Journal of Computational Physics , Vol 499 (2024) 112722.
  5. W.-F. Hu, Y.-J. Shih, T.-S. Lin, M.-C. Lai, A shallow physics-informed neural network for solving partial differential equations on static and evolving surfaces, Computer Methods in Applied Mechanics and Engineering, Vol 418 (2024) 116486. arXiv:2203.01581.
  6. P.-C. Kuo, M.-C. Lai, Y. Mori, A. Rodenberg, The tension determination problem for an inextensible interface in 2D Stokes flow, Research in the Mathematical Sciences (2023) 10:46. arXiv:2302.05062
  7. Y.-H. Tseng, M.-C. Lai, A discontinuity and cusp capturing PINN for Stokes interface problems with discontinuous viscosity and singular forces, Annals of Applied Mathematics, Vol 39 (2023) pp.385-403. (Invited article, dedicated to the memory of Prof. Zhongci Shi.) arXiv:2307.09236
  8. W.-F. Hu, T.-S. Lin, Y.-H. Tseng, M.-C. Lai, An efficient neural-network and finite-difference hybrid method for elliptic interface problems with applications, Communications in Computational Physics, Vol 33 (2023), pp. 1090--1105. arXiv:2210.05523.
  9. Y.-H. Tseng, T.-S. Lin, W.-F. Hu, M.-C. Lai, A cusp-capturing PINN for elliptic interface problems, Journal of Computational Physics, Vol 491 (2023), 112359. arXiv:2210.08424.
  10. W.-F. Hu, T.-S. Lin, M.-C. Lai, A discontinuity capturing shallow neural network for elliptic interface problems, Journal of Computational Physics, Vol 469 (2022), 111576. arXiv:2106.05587.
  11. M.-C. Lai, C.-C. Chang, W.-S. Lin, W.-F. Hu, T.-S. Lin, A shallow Ritz method for elliptic problems with singular sources, Journal of Computational Physics, Vol 469 (2022), 111547. arXiv:2107.12013.
  12. K. C. Ong, Y. Seol, M.-C. Lai, An immersed boundary projection method for solving the fluid-rigid body interaction problems, Journal of Computational Physics, Vol 466 (2022), 111367.
  13. M.-C. Lai, S. Park, Y. Seol, An energy stable finite difference method for anisotropic surface diffusion on closed curves, Applied Mathematics Letters, Vol 127 (2022), 107848.
  14. M.-C. Lai, Y. Seol, A stable and accurate immersed boundary method for simulating vesicle dynamics via spherical harmonics, Journal of Computational Physics, Vol 449 (2022), 110785.
  15. H. Nganguia, W.-F. Hu, M.-C. Lai, and Y.-N. Young, Effects of surfactant solubility on the hydrodynamics of a viscous drop in a dc electric field, Physical Review Fluids 6, (2021) 064004.
  16. K. C. Ong, M.-C. Lai, Y. Seol, An immersed boundary projection method for incompressible interface simulations in 3D flows, Journal of Computational Physics, Vol 430 (2021), 110090.
  17. Y. Seol, M.-C. Lai, Spectrally accurate algorithm for points redistribution on closed curves, SIAM Journal on Scientific Computing, Vol 42, No 5, (2020), pp. A3030-A3054.
  18. K. C. Ong, M.-C. Lai, An immersed boundary projection method for simulating the inextensible vesicle dynamics, Journal of Computational Physics, Vol 408 (2020), 109277.
  19. A. Farutin, H. Wu, W.-F. Hu, S. Rafai, P. Peyla, M.-C. Lai, and C. Misbah, Analytical Study for Swimmers in a Channel , Journal of Fluid Mechanics, Vol 881 (2019), pp. 365-383.
  20. S.-H. Hsu, W.-F. Hu, M.-C. Lai, A coupled immersed interface and grid based particle method for three-dimensional electrohydrodynamic simulations, Journal of Computational Physics, Vol 398 (2019), 108903.
  21. S.-H. Hsu, J. Chu, M.-C. Lai, R. Y.-H. Tsai, A coupled grid based particle and implicit boundary integral method for two-phase flows with insoluble surfactant, Journal of Computational Physics, Vol 395 (2019), pp. 747-764.
  22. M.-C. Lai, K. C. Ong, Unconditionally energy stable schemes for the inextensible interface problem with bending, SIAM Journal on Scientific Computing , Vol 41, No 4, (2019), pp. B649-B668.
  23. Y. Seol, Y.-H. Tseng, Y. Kim, M.-C. Lai, An immersed boundary method for simulating Newtonian vesicles in viscoelastic fluid, Journal of Computational Physics, Vol 376 (2019), pp. 1009-1027.
  24. M.-C. Lai, M.-C. Shiue, K. C. Ong, A simple projection method for the coupled Navier-Stokes and Darcy flows, Computational Geosciences , Vol 23 (2019), 21-33.
  25. Y. Kim, M.-C. Lai, Y. Seol, A penalty immersed boundary method for viscoelastic particulate flows , Journal of Non-Newtonian Fluid Mechanics , Vol 258 (2018), 32-44.
  26. W.-F. Hu, M.-C. Lai, C. Misbah, A coupled immersed boundary and immersed interface method for interfacial flows with soluble surfactant , Computers and Fluids , Vol 168 (2018), 201-215.
  27. M.-C. Shiue, K. C. Ong, M.-C. Lai, Convergence of the MAC scheme for the Stokes/Darcy coupling problem , Journal of Scientific Computing, Vol 76 (2018), 1216-1251.
  28. Z. Li, M.-C. Lai, X. Peng, Z. Zhang, A least squares augmented immersed interface method for solving Navier-Stokes and Darcy coupling equations, Computers and Fluids , Vol 167 (2018), 384-399.
  29. Y. Seol, S.-H. Hsu, M.-C. Lai, An immersed boundary method for simulating interfacial flows with insoluble surfactant in three dimensions, Communications in Computational Physics , Vol 23 (2018), pp. 640-664.
  30. J.-J. Xu, W. Shi, M.-C. Lai, A level-set method for two-phase flows with soluble surfactant, Journal of Computational Physics, Vol 353 (2018), pp. 336-355.
  31. Y. Kim, M.-C. Lai, and Y. Seol, Simulation of a soap film Mobius strip transformation, East Asian Journal on Applied Mathematics, Vol 7, No 3 (2017), pp. 615-628.
  32. Y. Kim, M.-C. Lai, and Y. Seol, Numerical simulations of vesicle and bubble dynamics in two-dimensional four-roll mill flows, Physical Review E 95 (2017), 053105.
  33. M.-C. Lai and Y. Seol, A short note on Navier-Stokes flows with an incompressible interface and its approximations, Applied Mathematics Letters, Vol 65 (2017), pp. 1-6.
  34. H. Wu, A. Farutin, W.-F. Hu, M. Thiebaud, S. Rafai, P. Peyla, M.-C. Lai, and C. Misbah, Amoeboid swimming in a channel , Soft Matter, 12 (2016), pp. 7470-7484.
  35. Y. Seol, W.-F. Hu, Y. Kim and M.-C. Lai, An immersed boundary method for simulating vesicle dynamics in three dimensions , Journal of Computational Physics, Vol 322 (2016), pp. 125-141.
  36. K.-L. Pan, Y.-H. Tseng, J.-C. Chen, K.-L. Huang, C.-H. Wang, and M.-C. Lai Controlling droplet bouncing and coalescence with surfactant, Journal of Fluid Mechanics, Vol 799 (2016), pp. 603-636.
  37. H. Nganguia, Y.-N. Young, A. T. Layton, M.-C. Lai, and W.-F. Hu, Electrohydrodynamics of a viscous drop with inertia, Physical Review E 93 (2016), 053114 .
  38. W.-F. Hu, M.-C. Lai, Y. Seol and Y.-N. Young, Vesicle electrohydrodynamic simulations by coupling immersed boundary and immersed interface method , Journal of Computational Physics, Vol 317 (2016), pp. 66-81.
  39. H. Wu, M. Thiebaud, W.-F. Hu, A. Farutin, S. Rafai, M.-C. Lai, P. Peyla, and C. Misbah, Amoeboid motion in confined geometry, Rapid Communications, Physical Review E 92 (2015), 050701(R).
  40. H. Nganguia, Y.-N. Young, A. T. Layton, W.-F. Hu, and M.-C. Lai, An immersed interface method for axisymmetric electrohydrodynamic simulations in Stokes flow, Communications in Computational Physics , Vol 18 (2015), pp. 429-449.
  41. W.-F. Hu, M.-C. Lai, and Y.-N. Young, A hybrid immersed boundary and immersed interface method for electrohydrodynamic simulations, Journal of Computational Physics, Vol 282 (2015), pp. 47-61.
  42. P.-W. Hsieh, M.-C. Lai, S.-Y. Yang, and C.-S. You, An unconditionally energy stable penalty immersed boundary method for simulating the dynamics of an inextensible interface interacting with a solid particle, Journal of Scientific Computing, Vol 64 (2015), pp. 289-316.
  43. K.-Y. Chen and M.-C. Lai, A conservative scheme for solving coupled surface-bulk convection-diffusion equations with an application to interfacial flows with soluble surfactant, Journal of Computational Physics, Vol 257 (2014), pp. 1-18.
  44. J.-J. Xu, Y. Huang, M.-C. Lai and Z. Li, A coupled immersed interface and level set method for three-dimensional interfacial flows with insoluble surfactant, Communications in Computational Physics , Vol 15, No 2 (2014), pp. 451-469.
  45. W.-F. Hu, Y. Kim, and M.-C. Lai, An immersed boundary method for simulating the dynamics of three-dimensional axisymmetric vesicles in Navier-Stokes flows, Journal of Computational Physics, Vol 257 (2014), pp. 670-686.
  46. Y. Kim, M.-C. Lai, C. S. Peskin and Y. Seol, Numerical simulations of three-dimensional foam by the immersed boundary method, Journal of Computational Physics, Vol 269 (2014), pp. 1-21.
  47. W.-F. Hu and M.-C. Lai, Unconditionally energy stable immersed boundary method with application to vesicle dynamics, East Asian Journal on Applied Mathematics, Vol 3, No 3 (2013), pp. 247-262.
  48. P. Constantin, M.-C. Lai, R. Sharma, Y.-H. Tseng and J. Wu, New Numerical Results for the Surface Quasi-Geostrophic Equation, Journal of Scientific Computing, Vol 50, Issue 1 (2012), 1-28.
  49. Y. Kim, Y. Seol, M.-C. Lai and C. S. Peskin, The immersed boundary method for two-dimensional foam with topological changes, Communications in Computational Physics , Vol 12, No 2 (2012), 479-493.
  50. C.-H. Teng, I.-L. Chern and M.-C. Lai, Simulating binary fluid-surfactant dynamics by a phase field model, Discrete and Continuous Dynamical Systems - Series B , Vol 17, No 4 (2012), 1289-1307.
  51. M.-C. Lai, W.-F. Hu, and W.-W. Lin, A fractional step immersed boundary method for Stokes flow with an inextensible interface enclosing a solid particle, SIAM Journal on Scientific Computing , Vol 34, No 5 (2012) pp.B692-B710.
  52. Y. Kim and M.-C. Lai, Numerical study for viscosity and inertial effects on vesicle tank-treading to tumbling motion under shear flow, Physical Review E 86 (2012), 066321.
  53. C.-T. Wu, Z. Li and M.-C. Lai, Adaptive mesh refinement for elliptic interface problems using the non-conforming immersed finite element method , International Journal of Numerical Analysis and Modeling, Vol 8, No 3 (2011), 466-483.
  54. M.-C. Lai, C.-Y. Huang and Y.-M. Huang, Simulating the axisymmetric interfacial flows with insoluble surfactant by immered boundary method , International Journal of Numerical Analysis and Modeling, Vol 8, No 1 (2011), 105-117.
  55. Z. Li and M.-C. Lai, New finite difference methods based on IIM for inextensible interfaces in incompressible flows , East Asian Journal on Applied Mathematics, Vol 1, No 2 (2011), 155-171.
  56. K.-Y. Chen, K.-A. Feng, Y. Kim and M.-C. Lai, A note on pressure accuracy in immersed boundary method for Stokes flow, Journal of Computational Physics, Vol 230 (2011), 4377-4383.
  57. Z. Li, M.-C. Lai, G. He and H. Zhao, An augmented method for free boundary problems with moving contact lines, Computers and Fluids , Vol 39 (2010), 1033-1040.
  58. Y. Kim, M.-C. Lai and C. S. Peskin, Numerical simulations of two-dimensional foam by the immersed boundary method, Journal of Computational Physics, Vol 229 (2010), 5194-5207.
  59. M.-C. Lai, Y.-H. Tseng and H. Huang, Numerical simulation of moving contact lines with surfactant by immersed boundary method , Communications in Computational Physics , Vol 8 (2010), 735-757.
  60. Y. Kim and M.-C. Lai, Simulating the dynamics of inextensible vesicles by the penalty immersed boundary method , Journal of Computational Physics, Vol 229 (2010), 4840-4853.
  61. K. Ito, M.-C. Lai and Z. Li A well-conditioned augmented system for solving Navier-Stokes equations in irregular domains, Journal of Computational Physics, Vol 228 (2009), 2616-2628.
  62. M.-C. Lai, C.-W. Hsu and H. Huang, A front-tracking method for motion by mean curvature with surfactant, Advances in Applied Mathematics and Mechanics, Vol 1, No 2 (2009), 288-300.
  63. M.-C Lai and H.-C. Tseng, A simple implementation of the immersed interface methods for Stokes flows with singular forces , Computers and Fluids , vol 37 (2008), 99-106.
  64. M.-C. Lai, Y.-H. Tseng and H. Huang, An immersed boundary method for interfacial flows with insoluble surfactant, Journal of Computational Physics, Vol 227 (2008), 7279-7293.
  65. H. Huang, M.-C. Lai and H.-C. Tseng, A parametric derivation of the surfactant transport equation along a deforming fluid interface, Frontiers of Applied and Computational Mathematics , ed. by D. Blackmore, A. Bose and P. Petropoulos, (2008) pp. 198--205.
  66. S.-W. Su, M.-C. Lai and C.-A. Lin, An immersed boundary technique for simulating complex flows with rigid boundary, Computers and Fluids , vol 36 (2007), 313-324.
  67. Z. Li, K. Ito and M.-C. Lai, An augmented approach for Stokes equations with discontinuous viscosity and singular forces , Computers and Fluids , vol 36 (2007), 622-635.
  68. M.-C. Lai and J.-M Tseng, A formally fourth-order accurate compact scheme for 3D Poisson equation in cylindrical coordinates , Journal of Computational and Applied Mathematics, vol 201 (2007), 175-181.
  69. M.-C. Lai, C.-T. Wu and Y.-H. Tseng, An efficient semi-coarsening multigrid method for variable diffusion problems in cylindrical coordinates , Applied Numerical Mathematics, vol 57 (2007), 801-810.
  70. M.-C. Lai, Z. Li and X. Lin, Fast solvers for 3D Poisson equations involving interfaces in a finite or the infinite domain, Journal of Computational and Applied Mathematics , vol 191 (2006), 106-125.
  71. J. Huang, M.-C. Lai and Y. Xiang, An integral equation method for epitaxial step flow growth simulations , Journal of Computational Physics, vol 216 (2006), 724-743.
  72. M.-C. Lai and Y.-H. Tseng, A fast iterative solver for the variable coefficient diffusion equation on a disk , Journal of Computational Physics, vol 208 (2005), 196-205.
  73. M.-C. Lai and H.-C. Liu, Fast direct solver for the biharmonic equation on a disk and its application to incompressible flows, Applied Mathematics and Computation, vol 164 (2005), 679-695.
  74. M.-C. Lai, Fast direct solver for Poisson equation in a 2D elliptical domain, Numerical Methods for Partial Differential Equations , vol 20 (2004), 72-81.
  75. M.-C. Lai, C.-Y. Huang and T.-S. Lin, A simple Dufort-Frankel type scheme for the Gross-Pitaevskii equation of Bose-Einstein condensates on different geometries , Numerical Methods for Partial Differential Equations , vol 20, No 4 (2004), 624-638.
  76. Z. Li, W.-C. Wang, I.-L. Chern and M.-C. Lai, New formulations for interface problems in polar coordinates, SIAM J. on Scientific Computing, vol 25, No 1 (2003), 224-245.
  77. K.-H. Chiam, M.-C. Lai and H. S. Greenside, Efficient algorithm on a nonstaggered mesh for simulating Rayleigh-Benard convection in a box , Physical Review E , 68 (2003), 026705.
  78. M.-C. Lai, Fourth-order finite difference scheme for the incompressible Navier-Stokes equations in a disk , International Journal for Numerical Methods in Fluids , vol. 42 (2003), 909-922.
  79. M.-C. Lai, Fast Poisson solver in a three-dimensional ellipsoid , Contemporary Mathematics , AMS, vol 329 (2003), 203-208.
  80. M.-C. Lai and W.-C. Wang, Fast direct solvers for Poisson equation on 2D polar and spherical geometries , Numerical Methods for Partial Differential Equations vol 18 (2002), 56-68.
  81. M.-C. Lai, W.-W. Lin and W. Wang, A fast spectral/difference method without pole conditions for Poisson-type equations in cylindrical and spherical geometries , IMA J. of Numerical Analysis, vol 22, No 4 (2002), 537-548.
  82. M.-C. Lai, A simple compact fourth-order Poisson solver on polar geometry , Journal of Computational Physics, vol 182 (2002), 337-345.
  83. M.-C. Lai and Z. Li, A remark on jump conditions for the three-dimensional Navier-Stokes equations involving an immersed moving membrane , Applied Mathematics Letters 14, vol 2 (2001), 149-154.
  84. J. T. Beale and M.-C. Lai, A method for computing nearly singular integrals , SIAM J. on Numerical Analysis, vol 38, No 6 (2001), 1902-1925.
  85. M.-C. Lai, A note on finite difference discretizations for Poisson equation on a disk , Numerical Methods for Partial Differential Equations, vol 17, issue 3 (2001), 199-203.
  86. Z. Li and M.-C. Lai, The immersed interface method for the Navier-Stokes equations with singular forces , Journal of Computational Physics, vol 171, No 2 (2001), 822-842.
  87. M.-C. Lai and C. S. Peskin, An immersed boundary method with formal second-order accuracy and reduced numerical viscosity, Journal of Computational Physics, 160 (2000), 705-719.
Selected Visits and Talks: (no updated since 2018)