1. Multiscale method and computation
2. Scientific Machine Learning
Ph.D, Texas A&M University, 2008
2018/01-present School of Mathematical Sciences, Tongji University, Professor
2013/02-2017/12 Institute of Mathematics, Hunan University, Professor
2008/09-2010/08 IMA, University of Minnesota, Postdoctoral fellow
Some works in recent 3 years :
Mengnan Li and Lijian Jiang*, Deep learning nonlinear multiscale dynamic problems using Koopman operator, Journal of Computational Physics, 446 (2021), 110660.
Yuming Ba and Lijian Jiang*, A two-stage variable-separation Kalman filter for data assimilation, Journal of Computational Physics, 434 (2021), 110244.
Xiaoyan Song, Guang-hui Zheng, Lijian Jiang*, Variational Bayesian inversion for the reaction coefficient in space-time nonlocal diffusion equations, Advances in Computational Mathematics, 47 (2021)，31
Lijian Jiang, Lingling Ma*, A hybrid model reduction method for stochastic parabolic optimal control problems，Computer Methods in Applied Mechanics and Engineering, 370 (2020), 113244.
Lijian Jiang*, Mengnan Li, Model reduction for nonlinear multiscale parabolic problems using dynamic mode decomposition, International Journal for Numerical Methods in Engineering, 121 (2020), pp. 3680-3701.
Na Ou, Guang Lin and Lijian Jiang*, A low-rank approximated multiscale method for PDEs with random coefficients, Multiscale Modeling and Simulation, 18（2020），pp. 1595-1620.
Mengnan Li, Eric Chung and Lijian Jiang*, A constraint energy minimizing generalized multiscale finite element method for parabolic equations, Multiscale Modeling and Simulation, 17 (2019), pp.996-1018.
Fuchen Chen, Eric Chung, Lijian Jiang*, Adaptive least-squares mixed generalized multiscale finite element methods, Multiscale Modeling and Simulation, 16 (2018), pp. 1034-1058.
Yuming Ba, Lijian Jiang*, Na Ou, A two-stage ensemble Kalman filter based on multiscale model reduction for inverse problems in time fractional diffusion-wave equations, Journal of Computational Physics, 374 (2018), pp. 300-330.
Qiuqi Li and Lijian Jiang*, A novel variable-separation method based on sparse representation for stochastic partial differential equations, SIAM Journal on Scientific Computing, 39 (2017), pp. A2879-2910.
Granted projects in progress:
1. Stochastic multiscale model reduction and its applications, NSFC, PI.
2. Bayesian uncertainty quantification for random porous media models, NSFC, PI
Associate Editor: Journal of Computational and Applied Mathematics
Associate Editor: Journal on Numerical Methods and Computer Applications
Associate Editor: Journal of Computational Mathematics and Data Science
I am looking for graduate students (master and Ph.D) to join our research group. Senior undergraduate students are also welcome. Our research attempts to develop, analyze and implement novel numerical methods, statistical methods and machine learning for multiscale models and stochastic models, and investigates their applications in applied sciences and engineering. Interdisciplinary research is our preference. Research assistanceship is provided.