Submitted
⭐ ⭐ ⭐ 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
- F. Lu, M. Maggioni and S. Tang: Learning interaction kernels in heterogeneous systems of agents from multiple trajectories.   arXiv1910 To appear on JMLR. 2021
- 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
- F. Lu. Data-driven model reduction for stochastic Burgers equations. Entropy, 22(12), 1360, 2020. arXiv2010 Journal   PDF
- 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
- 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
- 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
- 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)
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- F. Lu. Branching points for a class of variational equations involving potential with parameter. Adv. Nonlinear Stud. 8 (2008), no. 2, 251--269.