数学学院

Research Interests（ResearchID，Google scholar）

－Bayesian modeling and computation

－Stochastic computations and uncertainty quantification

－Inverse and ill-posed problems

－Scientific machine learning

Submitted:

4. Y.Y. Wang, L.Yan,T. Zhou,Deep learning-enhanced reduced-order ensemble Kalman filter for efficient Bayesian data assimilation of parametric PDEs, 2024.

3. Y. W.Yin, L. Yan, A novel direct imaging method for passive inverse obstacle scattering problem, 2024.

2. Y.W. Yin, L. Yan, Physics-aware deep learning framework for the limited aperture 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:

40. Z.W. Gao, L. Yan, T. Zhou, Adaptive operator learning for infinite-dimensional Bayesian inverse problems, to appear in SIAM/ASA Journal on Uncertainty Quantification, 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).

35. Z.W. Gao(高志伟), L. Yan, T. Zhou, Failure-informed adaptive sampling for PINNs, SIAM J. Sci. Comput., 45(4): A1971-A1994, 2023.

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, Journal of Computational Physics, 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.

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. Journal of Computational Physics,, 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.