招生方向：数学、统计（熟练C++、Python编程优先）
硕士研究生----深度贝叶斯方法(深度学习+贝叶斯); 科学机器学习方法；不确定性量化方法及应用；
统计反问题；数据同化；多保真建模及在可靠性分析、验证与确认（V&V）中的应用.
博士研究生----深度贝叶斯方法：理论、算法及其实现.
博士后----- 不确定性量化；贝叶斯建模及计算；科学机器学习
研究方向：不确定性量化、PDE反问题、贝叶斯建模及计算、科学机器学习
Research Interests（ResearchID，Google scholar）
－Uncertainty quantification
－Inverse and ill-posed problems
－Bayesian modeling and computation
－Scientific machine learning
Submitted:
3. Y.Y. Wang, L.Yan, T. Zhou, Deep learning-enhanced reduced-order ensemble Kalman filter for efficient Bayesian data assimilation of parametric PDEs, 2024.
2. Y. W.Yin, L. Yan, A novel direct imaging method for passive inverse obstacle scattering problem, 2024.
1. Y.Y. Wang, L.Yan, Data-driven operator inference for parameter estimation in nonlinear partial differential equation,2024.
Journal Papers:
41. Y.W. Yin, L. Yan, Physics-aware deep learning framework for the limited aperture inverse obstacle scattering problem, to appear in SIAM J. Sci. Comput., 2024.
40. Z.W. Gao, L. Yan, T. Zhou, Adaptive operator learning for infinite-dimensional Bayesian inverse problems, SIAM/ASA Journal on Uncertainty Quantification, 12(4):1389-1423,2024.
39. Y.W. Yin (尹运文), L. Yan, Bayesian model error method for the passive inverse scattering problem, Inverse Problem, 40: 065005, 2024.
38. H. Gu(顾昊), X. Xu, L. Yan, Inverse elastic scattering by random periodic structures, Journal of Computational Physics, 501:112785,2024.
37. W.B. Liu, L. Yan, T. Zhou, Y.C. Zhou, Failure-informed adaptive sampling for PINNs, Part III: applications to inverse problems, CSIAM Transactions on Applied Mathematics,5(3):636-670, 2024.
36. Z.W. Gao, T. Tang, L. Yan, T. Zhou, Failure-informed adaptive sampling for PINNs, Part II: combining with re-sampling and subset simulation, Communications on Applied Mathematics and Computation, 6: 1720-1741, 2024 (Invited contribution to a special issue for Prof. Remi Abgrall 's 61th birthday).
34. Y. Y. Wang(王艳艳), Q. Li(李倩), L.Yan, Adaptive ensemble Kalman inversion with statistical linearization, Communications in Computational Physics, 33:1357-1380,2023.
33. Y.C. Li(李勇超),Y. Y. Wang(王艳艳), L.Yan, Surrogate modeling for Bayesian inverse problems based on physics-informed neural networks, Journal of Computational Physics, 475:111841,2023.
32. L. Yan, T. Zhou, Stein variational gradient descent with local approximations, Computer Methods in Applied Mechanics and Engineering, 386:114087,2021.
31. L. Yan, X.L. Zou(邹熙灵), Gradient-free Stein variational gradient descent with kernel approximation, Applied Mathematics Letters, 121: 107465, 2021.
30. L. Yan, T. Zhou, An acceleration strategy for randomize-then-optimize sampling via deep neural networks, Journal of Computational Mathematics, 39(6):848-864, 2021.
29. A. Narayan, L. Yan, T. Zhou. Optimal design for the kernel interpolation: applications to uncertainty quantification, Journal of Computational Physics, 430:110094,2021.
28. L. Yan, T. Zhou, An adaptive surrogate modeling based on deep neural networks for large-scale Bayesian inverse problems, Communications in Computational Physics, 28:2180-2205,2020. (A special issue on Machine Learning for Scientific Computing)
27. F.L. Yang, L. Yan, A non-intrusive reduced basis EKI for time-fractional diffusion inverse problems, Acta Math. Appl.Sinica-English Serier, 36(1):183-202, 2020.(A special issue for IP)
26. L. Yan, T. Zhou. Adaptive multi-fidelity polynomial chaos approach to Bayesian inference in inverse problems, Journal of Computational Physics, 2019, 381: 110-128.
25. L.Yan, T. Zhou. An adaptive multi-fidelity PC-based ensemble Kalman inversion for inverse problems, International Journal for Uncertainty Quantification, 2019, 9(3):205-220.
24. Y.X. Zhang, J.X. Jian, L. Yan, Bayesian approach to a nonlinear inverse problem for time-space fractional diffusion equation, Inverse Problems, 2018, 34:125002(19pp).
23. F.L. Yang, L. Yan, L. Ling. Doubly stochastic radial basis function methods, J. Comput. Phy., 2018, 363: 87-97.
22. L. Guo, A. Narayan, L. Yan, T. Zhou.Weighted approximate Fekete points: sampling for least-squares polynomial approximation, SIAM J. Sci. Comput., 2018, 40 (1), A366-A387.
21. L. Yan, Y. X. Zhang. Convergence analysis of surrogate-based methods for Bayesian inverse problems, Inverse Problems, 2017, 33:125001(20pp).
20. L. Guo, Y. Liu, L. Yan,Sparse recovery via lq-minimization for polynomial chaos expansions, Numer. Math. Theor. Meth. Appl., 2017,10(4):775-797.
19. L. Yan, Y. Shin, D. Xiu. Sparse approximation using L1-L2 minimization and its application to stochastic collocation SIAM J. Sci. Comput., 2017,39(1): A229–A254.
18. Y.X.Zhang, L. Yan. The general a posteriori truncation method and its application to radiogenic source identification for the Helium production-diffusion equation, Appl. Math. Model., 2017, 43 :126-138.
17. J.J. Liu, M. Yamamoto, L. Yan. On the reconstruction of unknown boundary sources for time fractional diffusion process by nonlocal measurement. Inverse Problems, 2016,32(1): 015009.
16. L. Yan, L. Guo. Stochastic collocation algorithms using l1-minimization for Bayesian solution of inverse problems, SIAM J. Sci. Comput., 2015,37(3), A1410–A1435.
15. L. Yan, F. L. Yang. The method of approximate particular solutions for the time-fractional diffusion equation with a non-local boundary condition, Comput. Math. Appl., 2015,70:254-264.
14. J.J.Liu, M. Yamamoto, L. Yan. On the uniqueness and reconstruction for an inverse problem of the fractional diffusion process, Appl. Numer. Math., 2015, 87:1-19.
13. L. Yan, F.L Yang. Efficient Kansa-type MFS algorithm for time-fractional inverse diffusion problems, Comput. Math. Appl.,2014, 67:1507-1520.
12. L. Yan, F.L. Yang. A Kansa-type MFS scheme for two-dimensional time fractional diffusion equations, Eng. Anal. Bound. Eleme., 2013, 37 (11): 1426–1435.
11. H. F. Zhao, L. Yan, J. J. Liu. On the interface identification of free boundary problem by method of fundamental solution. Numer. Linear Algebra Appl., 2013, 20(2)：385-396.
10. L. Yan, L. Guo, D.Xiu. Stochastic collocation algorithms using L1-minimization,Int. J. Uncertainty Quantification, 2012, 2(3): 279–293.(Highly Cited Paper)
9. L. Yan, F. L. Yang, C. L. Fu. A new numerical method for the inverse source problems from a Bayesian statistical perspective. Int. J. Numer. Meth. Eng., 2011, 85:1460-1474
8. Y.X. Zhang, C. L. Fu, L. Yan. Approximate inverse method for stable analytic continuation in a strip domain. J. Comput. Appl. Math., 2011, 235: 1979-1992
7. L. Yan, C. L. Fu, F. F. Dou. A computational method for identifying a spacewise-dependent heat source. Int. J. Numer. Meth. Biomedical Eng., 2010,26: 597-608
6. L. Yan, F. L.Yang, C.L.Fu. A meshless method for solving an inverse spacewise-dependent heat source problem. J. Comput. Phy., 2009, 228(1):123-136
5. F. L. Yang, L. Yan, T. Wei. The identification of a Robin coefficient by a conjugate gradient method. Int. J. Numer. Meth. Eng., 2009,78:800-816
4. L. Yan, F. L. Yang, C. L. Fu. A Bayesian inference approach to identify a Robin coefficient in one-dimensional parabolic problems. J. Comput. Appl. Math., 2009, 231(2):840-850
3. F. L. Yang, L. Yan, T. Wei. Reconstruction of part of a boundary for the Laplace equation by using a regularized method of fundamental solution. Inverse Problems Sci. Eng.,2009,17(8):1113-1128.
2. F. L. Yang, L. Yan, T. Wei. Reconstruction of the corrosion boundary for the Laplace equation by using a boundary collocation method. Math. Comput. Simu., 2009,79(7):2148-2156
1. L. Yan, C. L. Fu, F. L. Yang. The method of fundamental solutions for the inverse heat source problem. Eng. Anal. Bound. Elem., 2008, 32(3) :216-222.
