一、基本资料

1984年5月生，汉族，吉林省长春市人，中共党员，副教授，理学博士，新加坡南洋理工大学博士后，数学、应用统计专业硕士研究生导师。

二、教育背景与工作经历

2003年9月-2007年7月：哈尔滨工程大学，数学科学学院，理学学士

2007年9月-2009年7月：哈尔滨工程大学，数学科学学院，理学硕士

2009年9月-2014年7月：哈尔滨工业大学，数学学院，理学博士

2014年7月-2021年12月：东北大学，秦皇岛分校数学与统计学院，讲师

2022年1月至今：东北大学，秦皇岛分校数学与统计学院，副教授

三、合作研究经历

2022年7月-2023年7月：新加坡南洋理工大学，电气与电子工程学院，博士后

四、主讲课程和研究方向

本科生课程：

实变函数、数学物理方程、数学物理方程与特殊函数、线性代数、复变函数与积分变换

研究生课程：

神经网络导论

研究方向：

人工智能、应用数学、地球物理学/金融学/医学/光学的交叉学科研究，包括深度学习（CNN、GAN、PINN）、强化学习（AlphaGo）、多尺度方法（多重网格、小波）、同伦方法、反问题。

五、主要成果和荣誉

作为项目负责人主持省部级科研项目6项（河北省自然科学基金项目2项、河北省高等学校科学研究项目1项、中央高校基本科研业务费项目3项）、横向科研项目5项、河北省研究生教育教学改革研究项目1项、东北大学校级科研项目1项。

发表SCI检索国际学术期刊论文50余篇，EI检索国际学术会议论文30余篇，主编出版英文学术专著2部。

主要论文：

[1] 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. (SCI, JCR一区)

[2] 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. (SCI, JCR一区)

[3] Y. Hu, J. Xu, T. Liu, The impact of digitalization on carbon emission efficiency: An intrinsic Gaussian process regression approach, Sustainability, 2025, 17, 6551. (SSCI, SCI, JCR二区)

[4] 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. (SCI, JCR一区)

[5] 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. (SCI, JCR一区)

[6] 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. (SCI, JCR一区)

[7] W. Sun, J. Xu, T. Liu, Partially functional linear regression based on Gaussian process prior and ensemble learning, Mathematics, 2025, 13, 853. (SCI, JCR一区)

[8] 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. (SCI, JCR一区)

[9] 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. (SCI, JCR一区)

[10] 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. (SCI, JCR一区)

[11] 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. (SCI, JCR一区)

[12] 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. (SCI, JCR一区)

[13] 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. (SCI, JCR一区, TOP期刊)

[14] 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. (SCI, JCR一区, TOP期刊)

[15] 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. (SCI, JCR一区)

[16] 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. (SCI, JCR一区)

[17] 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. (SCI, JCR一区)

[18] 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. (SCI, JCR一区)

[19] 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. (SCI, JCR一区)

[20] 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. (SCI, JCR一区)

[21] 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. (SCI, JCR一区)

[22] W. Liu, B. Zhang, T. Liu, J. Jiang, Y. Liu, Artificial intelligence in pancreatic image analysis: A review, Sensors, 2024, 24, 4749. (SCI, JCR二区)

[23] S. Liu, T. Liu, Q. Ma, On a backward problem for the Rayleigh-Stokes equation with a fractional derivative, Axioms, 2024, 13, 30. (SCI, JCR一区)

[24] Y. Shi, R. Yan, T. Liu, A conservative difference scheme for solving the coupled fractional Schrödinger-Boussinesq system, Axioms, 2024, 13, 400. (SCI, JCR一区)

[25] 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. (SCI, JCR一区)

[26] 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. (SCI, JCR一区)

[27] 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. (SCI, JCR一区)

[28] T. Liu, Z. Ding, J. Yu, W. Zhang, Parameter estimation for nonlinear diffusion problems by the constrained homotopy method, Mathematics, 2023, 11, 2642. (SCI, JCR一区)

[29] 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. (SCI, JCR一区)

[30] 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. (SCI, JCR二区)

[31] 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. (SCI, JCR一区)

[32] Y. Sun, G. Zhang, Z. Wang, T. Liu, Convergence of the Euler method for impulsive neutral delay differential equations, Mathematics, 2023, 11, 4684. (SCI, JCR一区)

[33] T. Liu, Porosity reconstruction based on Biot elastic model of porous media by homotopy perturbation method, Chaos, Solitons and Fractals, 2022, 158, 112007. (SCI, JCR一区, TOP期刊)

[34] T. Liu, Parameter estimation with the multigrid-homotopy method for a nonlinear diffusion equation, Journal of Computational and Applied Mathematics, 2022, 413, 114393. (SCI, JCR一区, TOP期刊)

[35] 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. (SCI, JCR一区)

[36] 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. (SCI, JCR一区)

[37] 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. (SCI, JCR二区)

[38] T. Liu, A multigrid-homotopy method for nonlinear inverse problems, Computers and Mathematics with Applications, 2020, 79, 1706-1717. (SCI, JCR一区, TOP期刊)

[39] 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. (SCI, JCR一区, TOP期刊)

[40] T. Liu, A nonlinear multigrid method for inverse problem in the multiphase porous media flow, Applied Mathematics and Computation, 2018, 320, 271-281. (SCI, JCR一区, TOP期刊)

[41] 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. (SCI, JCR一区)

[42] 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. (SCI, JCR二区)

[43] 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. (SCI, JCR二区)

[44] 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. (SCI, JCR一区, TOP期刊)

[45] 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. (SCI, JCR一区, TOP期刊)

[46] 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. (SCI, JCR一区)

[47] 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. (SCI, JCR一区)

[48] 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. (SCI, JCR二区)

[49] 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. (SCI, JCR二区)

[50] 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. (SCI, JCR一区)

[51] 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. (SCI, JCR二区)

[52] 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. (SCI, JCR一区)

[53] 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. (SCI, JCR一区)

[54] 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. (SCI, JCR二区)

[55] 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. (SCI, JCR二区)

[56] 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. (SCI, JCR一区)

主要项目：

[1] 冀东地区中酸性岩体含矿性识别深度学习模型构建，河北省地质矿产勘查开发局项目，主持

[2] 基于人工智能的河北省山区地热资源与地震相关性研究，河北省地质矿产勘查开发局项目，主持

[3] 基于人工智能的渤海湾盆地北缘地震与地热资源相关性分析，河北宝地建设工程有限公司项目，主持

[4] 人工智能背景下多学科交叉创新型研究生人才培养模式研究，河北省研究生教育教学改革研究项目，主持

[5] 深部真菌感染快速智能成像分析系统的研制与产业化，江苏省苏州高新区狮山科技创业领军人才（孵化）项目，合作（吉林大学）

[6] 孢子丝菌病体外镜检荧光试剂研发与应用创新团队，吉林省科技厅项目，合作（吉林大学）

[7] 基于深度学习的秦皇岛海域常见赤潮藻种图像识别技术研究，海洋岸线生态修复与智慧海洋监测河北省工程研究中心开放课题，主持

[8] 基于流体渗流-物理（电阻率）耦合模拟的环渤海地区深部超临界地热能源特征分析，河北省地质矿产勘查开发局项目，主持

[9] 流体饱和多孔介质参数反演的全变差正则化方法研究，中央高校基本科研业务费国家项目培育基金，主持

[10] 基于流体质量平衡方程的储层参数反演的重构模型和算法研究，河北省自然科学基金面上项目，主持

[11] 非线性对流-扩散方程反问题的同伦混合方法研究，中央高校基本科研业务费国家项目培育基金，主持

[12] 非线性扩散方程反演问题的同伦混合优化方法研究，河北省自然科学基金青年科学基金，主持

[13] 非线性扩散方程渗透率反演的小波多重网格方法，河北省高等学校科学研究项目，主持

[14] 多孔多相介质流渗透率反演的多尺度方法研究，中央高校基本科研业务费青年教师科研启动基金，主持

[15] 半线性微分方程的数值理论及其应用，国家自然科学基金面上项目，参与

主要著作：

[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.

荣誉：

[1] 2020年  河北省自然科学基金结题验收优秀项目

[2] 2021，2022，2023，2025年  东北大学秦皇岛分校本科生毕业设计优秀指导教师

[3] 2021，2022，2024年  东北大学秦皇岛分校创新创业教育优秀指导教师

[4] 指导学生参加全国大学生数学建模竞赛获得国家二等奖1项，省一等奖4项，省二等奖3项

[5] 指导学生参加美国大学生数学建模竞赛获得特等奖1项，一等奖2项，二等奖9项

[6] 指导学生参加“挑战杯”全国大学生课外学术科技作品竞赛获得省二等奖1项

学术报告：

[1] 2021年12月，新加坡科技研究局A*STAR作特邀学术报告，报告题目：Multigrid, Wavelet, Homotopy Methods for Optimization and Inverse Problems

[2] 2023年5月，第六届统计、数学建模与分析学术研讨会作特邀学术报告，报告题目：Multigrid-Homotopy Method for PDE-Based Inverse Problems

[3] 2025年5月，秦皇岛市第一医院作特邀学术报告，报告题目：AI技术在医学实践中的创新应用与成果

六、主要社会团体兼职

[1] 美国数学会《数学评论》（Mathematical Reviews）评论员

[2] SCI期刊《Mathematics》专题咨询委员

[3] SCI期刊《Mathematics》专刊“Advances in Computational Mathematics and Applied Mathematics”客座编辑

[4] SCI期刊《Mathematics》专刊“Advances in Computational Mathematics and Applied Mathematics, 2nd Editon”客座编辑

[5] SCI期刊《Axioms》专刊“Differential Equations and Inverse Problems”客座编辑

[6] SCI期刊《Axioms》专刊“Differential Equations and Inverse Problems, 2nd Editon”客座编辑

[7] 学术期刊《Annals of Mathematics and Physics》编委

[8] 学术期刊《Current Artificial Intelligence》编委

[9] 学术期刊《Journal of Advances in Applied & Computational Mathematics》编委

[10] 学术期刊《Journal of Information and Computing》编委

[11] 学术期刊《Journal of Nuclear Science and Technology Updates》编委

[12] 学术期刊《Medical Data Mining》青年编委

[13] PSG College of Arts & Science研究生论文外审专家

[14] EI会议2025 International Conference on Optical Engineering, Sensing and Instruments分论坛主席

[15] EI会议2023 International Conference on Intelligent Computing and Technology Applications客座编辑

[16] 全国本科毕业论文（设计）抽检评审专家

[17] 国研评审中心评审专家

[18] 以下EI会议编委：AMMAI 2025、OTOLARYNGOLOGY 2025、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

[19] 以下SCI期刊审稿人：AIMS Mathematics、Applied Mathematics and Computation、Applied Sciences、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、Sustainability、Symmetry

七、联系方式

电子邮箱：liutao@neuq.edu.cn