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  • ⭐ ⭐ ⭐ Xingjie Li, F. Lu and Felix X.F. Ye. ISALT: Inference-based schemes adaptive to large time-stepping for locally Lipschitz ergodic systems.   arXiv2102   PDF
  • ⭐ ⭐ ⭐ Zhongyang Li and F. Lu. On the coercivity condition in the learning of interacting particle systems.   arXiv2011   PDF
  • ⭐ ⭐ ⭐ Quanjun Lang and F. Lu. Learning interaction kernels in mean-field equations of 1st-order systems of interacting particles. arXiv2010   PDF
  • F. Lu, M. Maggioni and S. Tang. Learning interaction kernels in stochastic systems of interacting particles from multiple trajectories. arXiv2007

  • Published

    1. F. Lu, M. Maggioni and S. Tang: Learning interaction kernels in heterogeneous systems of agents from multiple trajectories.   arXiv1910 To appear on JMLR. 2021
    2. Zehong Zhang and F. Lu, Cluster prediction for opinion dynamics from partial observations. IEEE Transactions on Signal and Information Processing over Networks. vol 7, 101-113, 2021. arXiv2007 Journal
    3. F. Lu. Data-driven model reduction for stochastic Burgers equations. Entropy, 22(12), 1360, 2020. arXiv2010 Journal   PDF
    4. Z. Li, F. Lu, M. Maggioni, S. Tang and C. Zhang: On the identifiability of interaction functions in systems of interacting particles. Stoch.Process.Their Appl. 132, 135-163, 2021. arXiv1912 Journal PDF
    5. K.K. Lin and F. Lu. Data-driven model reduction, Wiener projections, and the Koopman-Mori-Zwanzig formalism.   J. Comput. Phys. 424, 109864, 2021. arXiv1908   Journal   PDF
    6. F. Lu, N. Weitzel and A. Monahan. Joint state-parameter estimation of a nonlinear stochastic energy balance model from sparse noisy data. Nonlin. Processes Geophys., 26, 227- 250, 2019. Journal   PDF
    7. F. Lu, M Zhong, S Tang and M Maggioni. Nonparametric inference of interaction laws in systems of agents from trajectory data. Proc. Natl. Acad. Sci. USA. 116 (29) 14424--14433. 2019 Journal   PDF (SI)
    8. F. Lu, X. Tu and A. J. Chorin. Accounting for model error from unresolved scales in ensemble Kalman filters by stochastic parametrization. Mon. Wea. Rev., 145(2017), no. 9, 3709--3723. Journal   PDF
    9. F. Lu, K. K. Lin and A. J. Chorin. Data-based stochastic model reduction for the Kuramoto--Sivashinsky equation. Physica D, 340 (2017), 46--57. Journal   PDF
    10. F. Lu, K. K. Lin and A. J. Chorin. Comparison of continuous and discrete-time data-based modeling for hypoelliptic systems. Comm. App. Math. Com. Sc., 11 (2016), no. 2, 187--216. Journal   PDF
    11. A. J. Chorin, F. Lu, R. N. Miller, M. Morzfeld and X. Tu. Sampling, feasibility, and priors in data assimilation. Discrete Contin. Dyn. Syst. Ser. A, 36 (2016), no. 8, 4227--4246. Journal   PDF
    12. A. J. Chorin and F. Lu. Discrete approach to stochastic parametrization and dimension reduction in nonlinear dynamics. Proc. Natl. Acad. Sci. USA, 112 (2015), no. 32, 9804--9809. Journal   PDF
    13. F. Lu, M. Morzfeld, X. Tu and A. J. Chorin. Limitations of polynomial chaos expansions in the Bayesian solution of inverse problems. J. Comput. Phys. 282 (2015), 138--147. Journal   PDF
    14. Y. Hu, F. Lu and D. Nualart. Convergence of Densities of functionals of Gaussian Processes. J. Funct. Anal. 266 (2014), no. 2, 814--875. Journal   PDF
    15. Y. Hu, F. Lu and D. Nualart. Non-degeneracy of Sobolev Pseudo-norms of fractional Brownian motions. Electron. Commun. Probab. 18(2013), no.84, 1--8.Journal   PDF
    16. Y. Hu, F. Lu and D. Nualart. Holder continuity of the solution for a class of nonlinear SPDEs arising from one-dimensional superprocesses. Probab. Theory Related Fields 156 (2013), no.1-2, 27--49. Journal   PDF
    17. Y. Hu, F. Lu and D. Nualart. Feynman-Kac formula for the heat equation driven by fractional noise with Hurst parameter H<1/2. Ann. Probab. 40 (2012), No. 3, 1041--1068. Journal   PDF
    18. F. Lu. Branching points for a class of variational equations involving potential with parameter. Adv. Nonlinear Stud. 8 (2008), no. 2, 251--269.