柳陶，男，1984年5月，理學博士，副教授，數學博士研究生導師，數學、應用統計碩士研究生導師。

聯系方式

電子郵件：liutao@neuq.edu.cn

辦 公 室：科技樓5090

研究方向

人工智能、應用數學、地球物理學/金融學/醫學/光學的交叉學科研究，包括深度學習（CNN、GAN、PINN）、強化學習（AlphaGo）、多尺度方法（多重網格、小波）、同倫方法、反問題。

教育背景

2003.09-2007.07 哈爾濱工程大學 數學與應用數學 理學學士；

2007.09-2009.07 哈爾濱工程大學 應用數學 理學碩士；

2009.09-2014.07 哈爾濱工業大學 數學 理學博士；

工作履歷

2022.07-2023.07 新加坡南洋理工大學 電氣與電子工程學院 博士后；

2014.07-今天 威尼斯wnsr9778秦皇島分校 數學與統計學院 講師、副教授；

學術兼職

美國數學會《數學評論》（Mathematical Reviews）評論員；

SCI期刊《Mathematics》專題咨詢委員；

SCI期刊《Mathematics》專刊“Advances in Computational Mathematics and Applied Mathematics”客座編輯；

SCI期刊《Mathematics》專刊“Advances in Computational Mathematics and Applied Mathematics, 2nd Editon”客座編輯；

SCI期刊《Axioms》專刊“Differential Equations and Inverse Problems”客座編輯；

SCI期刊《Axioms》專刊“Differential Equations and Inverse Problems, 2nd Editon”客座編輯；

學術期刊《Annals of Mathematics and Physics》編委；

學術期刊《Current Artificial Intelligence》編委；

學術期刊《Journal of Advances in Applied & Computational Mathematics》編委；

學術期刊《Journal of Information and Computing》編委；

學術期刊《Journal of Nuclear Science and Technology Updates》編委；

學術期刊《Global Financial Economics Journal》編委；

學術期刊《Medical Data Mining》青年編委；

PSG College of Arts & Science研究生論文外審專家；

EI會議2025 International Conference on Optical Engineering, Sensing and Instruments分論壇主席；

EI會議2023 International Conference on Intelligent Computing and Technology Applications客座編輯；

全國本科畢業論文（設計）抽檢評審專家；

國研評審中心評審專家；

以下EI會議編委：AMMAI 2025、OTOLARYNGOLOGY2025、AMDS 2022-2024、AMMCS 2022-2024、ICANCT 2022-2024、IWEP 2023-2024、ICCEAD 2024、ICAIC 2024、ICARCE 2022-2023、AMICS 2022-2023、ICAMCS 2023、ICAMP 2023、ACSE 2023、CMME 2023、SMMA 2023、ICTA 2023、CMBDA 2022、CPRA 2022；

以下SCI期刊審稿人：AIMS Mathematics、Applied Mathematics and Computation、Applied Sciences、Applied Soft Computing、Axioms、Chaos Solitons and Fractals、Communications in Nonlinear Science and Numerical Simulation、Computer Modeling in Engineering and Sciences、Electronic Research Archive、Electronics、Energies、Engineering Computations、Engineering with Computers、Foundations、Fractal and Fractional、International Journal of Mechanical Sciences、International Journal of Non-Linear Mechanics、Inverse Problems in Science and Engineering、Journal of Applied Analysis、Journal of Applied Analysis and Computation、Journal of Applied and Computational Mechanics、Journal of Imaging Informatics in Medicine、Journal of Mathematics、Journal of Petroleum Science and Engineering、Kuwait Journal of Science、Mathematical Biosciences and Engineering、Mathematical Methods in the Applied Sciences、Mathematics、Multidimensional Systems and Signal Processing、Optimization、Sensors、SoftwareX、Sustainability、Symmetry；

河北省燕趙英才；

科研情況

【在研項目】

1. 冀東地區中酸性巖體含礦性識別深度學習模型構建，河北省地質礦產勘查開發局項目，主持；

2. 基于人工智能的河北省山區地熱資源與地震相關性研究，河北省地質礦產勘查開發局項目，主持；

3. 基于人工智能的渤海灣盆地北緣地震與地熱資源相關性分析，河北寶地建設工程有限公司項目，主持；

4. 人工智能背景下多學科交叉創新型研究生人才培養模式研究，河北省研究生教育教學改革研究項目，主持；

5. 深部真菌感染快速智能成像分析系統的研制與產業化，江蘇省蘇州高新區獅山科技創業領軍人才（孵化）項目，合作（吉林大學）；

6. 孢子絲菌病體外鏡檢熒光試劑研發與應用創新團隊，吉林省科技廳項目，合作（吉林大學）；

【結題項目】

1. 基于深度學習的秦皇島海域常見赤潮藻種圖像識別技術研究，海洋岸線生態修復與智慧海洋監測河北省工程研究中心開放課題，主持；

2. 基于流體滲流-物理（電阻率）耦合模擬的環渤海地區深部超臨界地熱能源特征分析，河北省地質礦產勘查開發局項目，主持；

3. 流體飽和多孔介質參數反演的全變差正則化方法研究，中央高校基本科研業務費國家項目培育基金，主持；

4. 基于流體質量平衡方程的儲層參數反演的重構模型和算法研究，河北省自然科學基金面上項目，主持；

5. 非線性對流-擴散方程反問題的同倫混合方法研究，中央高校基本科研業務費國家項目培育基金，主持；

6. 非線性擴散方程反演問題的同倫混合優化方法研究，河北省自然科學基金青年科學基金，主持；

7. 非線性擴散方程滲透率反演的小波多重網格方法，河北省高等學校科學研究項目，主持；

8. 多孔多相介質流滲透率反演的多尺度方法研究，中央高校基本科研業務費青年教師科研啟動基金，主持；

9. 半線性微分方程的數值理論及其應用，國家自然科學基金面上項目，參與；

獎勵與榮譽

1. 2020年 河北省自然科學基金結題驗收優秀項目；

2. 2021，2022，2023，2025年 威尼斯wnsr9778秦皇島分校本科生畢業設計優秀指導教師；

3. 2021，2022，2024年 威尼斯wnsr9778秦皇島分校創新創業教育優秀指導教師；

4. 指導學生參加全國大學生數學建模競賽獲得國家二等獎1項，省一等獎4項，省二等獎5項；

5. 指導學生參加美國大學生數學建模競賽獲得特等獎1項，一等獎2項，二等獎9項；

6. 指導學生參加“挑戰杯”全國大學生課外學術科技作品競賽獲得省二等獎1項；

學術成果

近年來，發表SCI檢索論文60余篇，EI檢索論文30余篇，主編出版英文學術專著2部。

【代表性學術論文】

1. T. Liu, B. Ding, A radial basis function neural network approach for solving a diffusion partial differential equation efficiently, Applied Mathematics and Computation, 2026, 509, 129651.

2. T. Liu, R. Xue, A convergent multi-step efficient iteration method to solve nonlinear equation systems, Journal of Applied Mathematics and Computing, 2025, 71, 2571-2588.

3. T. Liu, B. Ding, B.N. Saray, D.A. Juraev, E.E. Elsayed, On the pseudospectral method for solving the fractional Klein-Gordon equation using Legendre cardinal functions, Fractal and Fractional, 2025, 9, 177.

4. Y. Hu, J. Xu, T. Liu, The impact of digitalization on carbon emission efficiency: An intrinsic Gaussian process regression approach, Sustainability, 2025, 17, 6551.

5. J. Li, T. Liu, J. Xu, X. Hu, C. Xu, Y. Wei, Numerical investigation for the temporal fractional financial option pricing partial differential equation utilizing a multiquadric function, Fractal and Fractional, 2025, 9, 414.

6. J. Wang, H. Kang, T. Liu, The Teacher-Assistant-Student collaborative and competitive network for brain tumor segmentation with missing modalities, Diagnostics, 2025, 15, 1552.

7. S. Chen, Y. Peng, Y. Liu, P. Wang, T. Liu, Enhancing YOLOv11 with large kernel attention and multi-scale fusion for accurate small and multi-lesion bone tumor detection in radiographs, Diagnostics, 2025, 15, 1988.

8. B. Wang, Y. Zhang, J. Li, T. Liu, Assessing expected shortfall in risk analysis through generalized autoregressive conditional heteroskedasticity modeling and the application of the Gumbel distribution, Axioms, 2025, 14, 391.

9. W. Sun, J. Xu, T. Liu, Partially functional linear regression based on Gaussian process prior and ensemble learning, Mathematics, 2025, 13, 853.

10. J. Zhu, Y. Li, Y. Li, T. Liu, Q. Ma, Fourth-order iterative algorithms for the simultaneous calculation of matrix square roots and their inverses, Mathematics, 2025, 13, 3370.

11. R. Xue, Y. Li, E. Song, T. Liu, An enhanced method with memory derived from Newton's scheme in solving nonlinear equations: Higher R-order convergence and numerical performance, Axioms, 2025, 14, 387.

12. S. Wang, Z. Wang, Y. Qi, T. Liu, The derivation of a multiquadric variant solver for the three-dimensional Heston-Hull-White PDE, Axioms, 2025, 14, 231.

13. S. Wang, J. Zhu, T. Liu, Hermite finite difference through kernel approximations to efficiently solve nonlinear Black-Scholes model, Mathematics, 2025, 13, 2727.

14. S. Wang, Z. Wang, W. Xie, Y. Qi, T. Liu, An accelerated sixth-order procedure to determine the matrix sign function computationally, Mathematics, 2025, 13, 1080.

15. C. Zhang, B. Zhao, W. Ren, R. Cao, T. Liu, A sixth-order iterative scheme through weighted rational approximations for computing the matrix sign function, Mathematics, 2025, 13, 2849.

16. F. Soleymani, Q. Ma, T. Liu, Managing the risk via the chi-squared distribution in VaR and CVaR with the use in generalized autoregressive conditional heteroskedasticity model, Mathematics, 2025, 13, 1410.

17. Y. Liu, R. Xue, T. Liu, S. Wang, S. Shateyi, A quartically fast iteration solver with convergence analysis for numerically determining the sign of a matrix, AIMS Mathematics, 2025, 10, 14055-14070.

18. T. Liu, F. Soleymani, M.Z. Ullah, Solving multi-dimensional European option pricing problems by integrals of the inverse quadratic radial basis function on non-uniform meshes, Chaos, Solitons and Fractals, 2024, 185, 115156.

19. T. Liu, T. Li, M.Z. Ullah, On five-point equidistant stencils based on Gaussian function with application in numerical multi-dimensional option pricing, Computers and Mathematics with Applications, 2024, 176, 35-45.

20. T. Liu, R. Xue, B. Ding, D.A. Juraev, B.N. Saray, F. Soleymani, A novel and effective scheme for solving the fractional telegraph problem via the spectral element method, Fractal and Fractional, 2024, 8, 711.

21. T. Liu, B. Ding, S. Shateyi, Computing the set of RBF-FD weights within the integrals of a kernel-based function and its applications, Axioms, 2024, 13, 875.

22. T. Liu, T. Li, M.Z. Ullah, A.K. Alzahrani, S. Shateyi, An efficient iterative approach for Hermitian matrices having a fourth-order convergence rate to find the geometric mean, Mathematics, 2024, 12, 1772.

23. T. Liu, Z. Zhao, S. Ling, H. Chao, H.F. Nafchi, S. Shateyi, Efficient scheme for the economic Heston-Hull-White problem using novel RBF-FD coefficients derived from multiquadric function integrals, Mathematics, 2024, 12, 2234.

24. T. Liu, S. Shateyi, Efficient fourth-order weights in kernel-type methods without increasing the stencil size with an application in a time-dependent fractional PDE problem, Mathematics, 2024, 12, 1121.

25. J. Xu, Y. Lu, Y. Su, T. Liu, Y. Qi, W. Xie, Intrinsic functional partially linear Poisson regression model for count data, Axioms, 2024, 13, 795.

26. S. Wang, S. Ling, H. Chao, Y. Qi, W. Zhang, Q. Ma, T. Liu, Inverse problem for the nonlinear convection-diffusion equation by using the multigrid method and constraint data, Mathematics, 2024, 12, 2402.

27. W. Liu, B. Zhang, T. Liu, J. Jiang, Y. Liu, Artificial intelligence in pancreatic image analysis: A review, Sensors, 2024, 24, 4749.

28. S. Liu, T. Liu, Q. Ma, On a backward problem for the Rayleigh-Stokes equation with a fractional derivative, Axioms, 2024, 13, 30.

29. Y. Shi, R. Yan, T. Liu, A conservative difference scheme for solving the coupled fractional Schr?dinger-Boussinesq system, Axioms, 2024, 13, 400.

30. S. Wang, H. Xian, T. Liu, S. Shateyi, Solving nonlinear equation systems via a Steffensen-type higher-order method with memory, Mathematics, 2024, 12, 3655.

31. T. Liu, M.Z. Ullah, K.M.A. Alshahrani, S. Shateyi, From fractal behavior of iteration methods to an efficient solver for the sign of a matrix, Fractal and Fractional, 2023, 7, 32.

32. T. Liu, D. Ouyang, L. Guo, R. Qiu, Y. Qi, W. Xie, Q. Ma, C. Liu, Combination of multigrid with constraint data for inverse problem of nonlinear diffusion equation, Mathematics, 2023, 11, 2887.

33. T. Liu, Z. Ding, J. Yu, W. Zhang, Parameter estimation for nonlinear diffusion problems by the constrained homotopy method, Mathematics, 2023, 11, 2642.

34. T. Liu, M.Z. Ullah, S. Shateyi, C. Liu, Y. Yang, An efficient localized RBF-FD method to simulate the Heston-Hull-White PDE in finance, Mathematics, 2023, 11, 833.

35. C. Chen, W. Zhang, T. Liu, Z. Zhang, W. Lu, L. Wang, Y. Zheng, Z. Lin, Online identification of inertial parameters of a robot with partially combined links using IMU sensing, Mechatronics, 2023, 94, 103023.

36. G. Zhang, Z. Wang, Y. Sun, T. Liu, Asymptotical stability criteria for exact solutions and numerical solutions of nonlinear impulsive neutral delay differential equations, Axioms, 2023, 12, 988.

37. Y. Sun, G. Zhang, Z. Wang, T. Liu, Convergence of the Euler method for impulsive neutral delay differential equations, Mathematics, 2023, 11, 4684.

38. T. Liu, Porosity reconstruction based on Biot elastic model of porous media by homotopy perturbation method, Chaos, Solitons and Fractals, 2022, 158, 112007.

39. T. Liu, Parameter estimation with the multigrid-homotopy method for a nonlinear diffusion equation, Journal of Computational and Applied Mathematics, 2022, 413, 114393.

40. T. Liu, K. Xia, Y. Zheng, Y. Yang, R. Qiu, Y. Qi, C. Liu, A homotopy method for the constrained inverse problem in the multiphase porous media flow, Processes, 2022, 10, 1143.

41. T. Liu, J. Yu, Y. Zheng, C. Liu, Y. Yang, Y. Qi, A nonlinear multigrid method for the parameter identification problem of partial differential equations with constraints, Mathematics, 2022, 10, 2938.

42. T. Liu, R. Xue, C. Liu, Y. Qi, A regularization homotopy strategy for the constrained parameter inversion of partial differential equations, Entropy, 2021, 23, 1480.

43. T. Liu, A multigrid-homotopy method for nonlinear inverse problems, Computers and Mathematics with Applications, 2020, 79, 1706-1717.

44. T. Liu, A wavelet multiscale method for the inverse problem of a nonlinear convection-diffusion equation, Journal of Computational and Applied Mathematics, 2018, 330, 165-176.

45. T. Liu, A nonlinear multigrid method for inverse problem in the multiphase porous media flow, Applied Mathematics and Computation, 2018, 320, 271-281.

46. T. Liu, An adaptive multigrid conjugate gradient method for the inversion of a nonlinear convection-diffusion equation, Journal of Inverse and Ill-posed Problems, 2018, 26, 623-631.

47. T. Liu, S. Liu, Identification of diffusion parameters in a non-linear convection-diffusion equation using adaptive homotopy perturbation method, Inverse Problems in Science and Engineering, 2018, 26, 464-478.

48. T. Liu, J. Song, Estimation of a permeability field within the two-phase porous media flow using nonlinear multigrid method, Mathematical Problems in Engineering, 2017, 2017, 2945712.

49. T. Liu, A wavelet multiscale-homotopy method for the parameter identification problem of partial differential equations, Computers and Mathematics with Applications, 2016, 71, 1519-1523.

50. T. Liu, Reconstruction of a permeability field with the wavelet multiscale-homotopy method for a nonlinear convection-diffusion equation, Applied Mathematics and Computation, 2016, 275, 432-437.

51. J. Zhao, T. Liu, An adaptive multigrid conjugate gradient method for permeability identification of nonlinear diffusion equation, Journal of Inverse and Ill-posed Problems, 2016, 24, 89-97.

52. J. Zhao, S. Liu, T. Liu, Determining surface heat flux for noncharacteristic Cauchy problem for Laplace equation, Mathematics and Computers in Simulation, 2016, 129, 69-80.

53. J. Zhao, T. Liu, A wavelet multiscale-adaptive homotopy method for the inverse problem of nonlinear diffusion equation, Inverse Problems in Science and Engineering, 2015, 23, 617-634.

54. J. Zhao, S. Liu, T. Liu, A modified kernel method for solving Cauchy problem of two-dimensional heat conduction equation, Advances in Applied Mathematics and Mechanics, 2015, 7, 31-42.

55. J. Zhao, T. Liu, G. Feng, A nonlinear multigrid method for inversion of two-dimensional acoustic wave equation, Journal of Inverse and Ill-posed Problems, 2014, 22, 429-448.

56. J. Zhao, T. Liu, S. Liu, Identification of space-dependent permeability in nonlinear diffusion equation from interior measurements using wavelet multiscale method, Inverse Problems in Science and Engineering, 2014, 22, 507-529.

57. J. Zhao, S. Liu, T. Liu, An inverse problem for space-fractional backward diffusion problem, Mathematical Methods in the Applied Sciences, 2014, 37, 1147-1158.

58. J. Zhao, S. Liu, T. Liu, A comparison of regularization methods for identifying unknown source problem for the modified Helmholtz equation, Journal of Inverse and Ill-posed Problems, 2014, 22, 277-296.

59. J. Zhao, S. Liu, T. Liu, A new regularization method for Cauchy problem of elliptic equation, Complex Variables and Elliptic Equations: An International Journal, 2014, 59, 1302-1314.

60. J. Zhao, T. Liu, S. Liu, An adaptive homotopy method for permeability estimation of a nonlinear diffusion equation, Inverse Problems in Science and Engineering, 2013, 21, 585-604.

61. J. Zhao, S. Liu, T. Liu, Two Tikhonov-type regularization methods for inverse source problem on the Poisson equation, Mathematical Methods in the Applied Sciences, 2013, 36, 1399-1408.

【專著】

1. T. Liu, Q. Ma, S. Liu, Differential Equations and Inverse Problems, Multidisciplinary Digital Publishing Institute, 2025, https://www.mdpi.com/books/reprint/10510.

2. T. Liu, F. Soleymani, Q. Ma, Advances in Computational Mathematics and Applied Mathematics, Multidisciplinary Digital Publishing Institute, 2025, https://www.mdpi.com/books/reprint/11195.

【學術報告】

1. 2021年12月，新加坡科技研究局A*STAR作特邀學術報告，報告題目：Multigrid, Wavelet, Homotopy Methods for Optimization and Inverse Problems；

2. 2023年5月，第六屆統計、數學建模與分析學術研討會作特邀學術報告，報告題目：Multigrid-Homotopy Method for PDE-Based Inverse Problems；

3. 2025年5月，秦皇島市第一醫院作特邀學術報告，報告題目：AI技術在醫學實踐中的創新應用與成果；

講授課程情況

《神經網絡導論》

《數學物理方程》

《實變函數》

《數學物理方程與特殊函數》

《復變函數與積分變換》

《線性代數》

指導研究生情況

已畢業碩士研究生2人，在讀碩士研究生8人，聯合培養中國地質大學（北京）地球物理學博士研究生1人，吉林大學臨床醫學碩士研究生3人，四川大學統計學碩士研究生1人。