賴明治（Ming-Chih Lai）終身講座教授

聯絡方式

• Email: mclai@nycu.edu.tw
• 電話: 03-5131361，或分機：31361
• 傳真: 03-572-4679
• 地址: 新竹市大學路1001號 陽明交通大學 應用數學系
• 相關網站: https://jupiter.math.nycu.edu.tw/~mclai/  

近兩學期教授課程

• 113 學年度第一學期：
  • 數學機器學習專題


• 113 學年度第二學期：
  • 數學機器學習專題(二)

履歷

• 學歷
  • 美國紐約大學庫朗數學學院數學博士 (1993/09~1998/09)
  • 清華大學應用數學所碩士 (1988/09 ~ 1990/06)
  • 中興大學應用數學系學士 (1984/09 ~ 1988/06)
• 學術專長暨研究領域
  • 機器學習
  • 科學計算
  • 流體力學
  • 偏微分方程數值方法
• 學術經歷與榮譽

  學術經歷

  • 國科會自然科學與永續發展處處長 2024/08~
  • 陽明交通大學理學院院長 (2021/08 ~ 2024/07)
  • 陽明交通大學終身講座教授 (2021/01 ~)
  • 陽明交通大學國際半導體產業學院合聘教授 (2020/02 ~ 2024/07)
  • 陽明交通大學智慧科學暨綠能學院(AI學院)合聘教授(2019/08 ~ 2024/07)
  • 台灣工業與應用數學會理事長 (2018/06 ~ 2020/05 )
  • 中華民國數學會 理事長 (2016/01 ~ 2017/12 )
  • 理論科學研究中心數學組 副主任（2016/01 ~ 2020/12）
  • 交通大學 講座教授 (2014/12 ~ 2020/12)
  • 中央研究院合聘研究員 (2013/08 ~ )
  • 交通大學 特聘教授 (2011/06~ 2014/11)
  • 國科會自然處數學學門 召集人 (2012/01~ 2014/12)
  • SIAM 東亞分會(EASIAM)Vice President(2011/01~2012/12), President (2013/01~ 2014/12)
  • 香港浸會大學 訪問教授 (2013/01~2013/05)
  • 日本京都大學數理解析研究所 訪問教授 (2012/09~ 2012/12)
  • 交通大學數學建模與科學計算中心 主任(2009/08~2012/07, 2014/08 ~ )
  • 國科會自然處 數學學門審議委員(2009/01~2011/12)
  • 交通大學應用數學系 主任 (2007/08~2009/07)
  • 交通大學應用數學系 教授 (2005/08~)
  • 國科會數學研究推動中心審議委員(2005/01~2007/12 )
  • 國科會理論科學研究中心數學組學術委員(2005~2013)，執行委員 (2012~2013)
  • 交通大學應用數學系 副教授 (2002/08~2005/07)
  • 中正大學數學系助理教授 (1999/08~2002/07)
  • 美國杜克大學博士後研究 (1998/08~1999/07)

  學術榮譽：

  • 台灣工業與應用數學會會士 (2021)
  • 第22屆國立中興大學傑出校友 (2018)
  • 第21屆教育部國家講座主持人（2017）
  • 第58屆教育部學術獎 (2014)
  • 國科會傑出研究獎 (2011)
  • 100年度中華民國數學會 學術獎(2011)
  • 國科會傑出學者研究計畫(2009/08~2012/07)
  • 交通大學學術研究獎 (2005)
  • 國科會傑出研究獎 (2003)
  • 交通大學 理學院院長獎 (2003/10)
  • Kurt O. Friedrichs 傑出畢業論文獎: NYU-Courant Institute (1999/04)

  期刊編輯：

  • Communications in Computational Physics (IF=1.813), 2012 -
  • East Asian Journal on Applied Mathematics (IF=0.923), 2010 -
  • Taiwanese Journal of Mathematics, 2014/08 - 2017/07
  • Journal of Biological Systems, 2013 - 2015
  • Advances in Applied Mathematics and Mechanics, 2009 -2018/04 

著作選集

(A)   Refereed Papers：

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, East Asian Journal on Applied Mathematics, Vol 14 (2024), pp. 490-506. (Invited article for Special issue for the 25th anniversary of EASIAM.) arXiv:2306.06333v2
2. 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.
3. 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.
4. 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
5. 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
6. 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.
7. 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.
8. 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.
9. 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.
10. 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.
11. 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.
12. 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.
13. 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.
14. 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.
15. 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.
16. 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.
17. 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.
18. 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.
19. 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.
20. 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.
21. 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.
22. 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.
23. 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.
24. 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.
25. 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.
26. 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.
27. 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.
28. 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.
29. 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.
30. 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.
31. 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.
32. 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.
33. 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.
34. 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.
35. 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 .
36. 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.
37. 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).
38. 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.
39. 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.
40. 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.
41. 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.
42. 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.
43. 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.
44. 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.
45. 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.
46. 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.
47. 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.
48. 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.
49. 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.
50. 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.
51. 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.
52. 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.
53. 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.
54. 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.
55. 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.
56. 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.
57. 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.
58. 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.
59. 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.
60. 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.
61. 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.
62. 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.
63. 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.
64. 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.
65. 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.
66. 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.
67. 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.
68. 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.
69. 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.
70. 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.
71. 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.
72. 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.
73. 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.
74. 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.
75. 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.
76. 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.
77. M.-C. Lai, Fast Poisson solver in a three-dimensional ellipsoid , Contemporary Mathematics , AMS, vol 329 (2003), 203-208.
78. 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.
79. 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.
80. M.-C. Lai, A simple compact fourth-order Poisson solver on polar geometry , Journal of Computational Physics, vol 182 (2002), 337-345.
81. 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.
82. 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.
83. 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.
84. 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.
85. 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.

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