刘文楷

个人简介

刘文楷，男，汉族，主要研究方向为微分方程数值解，主要研究内容是针对分数阶偏微分方程和整数阶偏微分方程提出物理信息神经网络算法的改进框架。相关成果发表在Applied Mathematics and Computation、Computers & Mathematics with Applications、Engineering Analysis with Boundary Elements等期刊。

教育经历

2021年9月--2023年7月，内蒙古大学数学专业，硕士

2023年9月--2026年7月，硕博连读，内蒙古大学数学专业，博士

主讲课程

线性代数

科研论著

1. Wenkai Liu, Yang Liu, Physics-informed Bézier curve neural network for solving forward and inverse problems of nonlinear fractional partial differential equations. Engineering Analysis with Boundary Elements, 2026, 191: 106934.

2. Wenkai Liu, Yang Liu, VooPINN: Physics-informed neural network with variable-order operator for forward and inverse problems of time fractional partial differential equations. Applied Mathematics and Computation, 2026, 524: 130044.

3. Wenkai Liu, Fanhai Zeng, Hong Li, Yang Liu, ITPINN: Integral-trainable physics informed neural network for solving high-dimensional evolution non-local partial differential equations. Computers & Mathematics with Applications, 2026, 205: 282-317.

4. Wenkai Liu, Yang Liu, Hong Li, Zhimin Zhang, Physics-informed neural network combined with weighted square terms and two-phase training strategy for partial differential equations. Engineering Analysis with Boundary Elements, 2026, 183: 106596.

5. Wenkai Liu, Yang Liu, A physics-informed neural network based on the separation of variables for solving the distributed-order time-fractional advection–diffusion equation. Fractal and Fractional, 2025, 9(11): 712.

6. Wenkai Liu, Yang Liu, A forward progressive physics informed neural network with Taylor series expansion for solving evolution partial differential equations. AIMS Mathematics, 2025, 10(10): 24857-24900.

7. Wenkai Liu, Yang Liu, Hong Li, Yining Yang, Multi-output physics-informed neural network for one- and two-dimensional nonlinear time distributed-order models. Networks and Heterogeneous Media, 2023, 18(4): 1899-1918.

8. Wenkai Liu, Yang Liu, Hong Li, Time difference physics-informed neural network for fractional water wave models. Results in Applied Mathematics, 2023, 17: 100347.