Home Research Teaching Publications Presentations  

Submitted

  1. Quanjun Lang, Xiong Wang, F.Lu, and Mauro Maggioni. Learning Multi-type heterogeneous interacting particle systems. arXiv2602
  2. Luxuan Yang, F.Lu, Ting Gao, Wei Wei, and Jinqiao Duan. Learning Lévy density via adaptive RKHS regression with bi-level optimization. arXiv2512
  3. Haibo Li and F.Lu. Automatic reproducing kernel and regularization for learning convolution kernels. arXiv2507
  4. F.Lu and Yue Yu. Transformer learns the cross-task prior and regularization for in-context learning. arXiv2505     Podcast by Google NotebookLM     slides
  5. Sichong Zhang, Xiong Wang, and F.Lu. Minimax rates for learning kernels in operators. arXiv2502     Podcast by Google NotebookLM
  6. Yuan Gao, Quanjun Lang, and F.Lu. Self-test loss functions for learning weak-form operators and gradient flows. arXiv2412
  7. Xiong Wang, Inbar Serrousi, and F.Lu. Optimal Minimax Rates for Learning Interaction Kernels. arXiv2311   PDF  
  8. Quanjun Lang and F.Lu. Small noise analysis for Tikhonov and RKHS regularizations. arXiv2305   PDF  

Other preprints

  1. Zehong Zhang, F.Lu, Esther Xu Fei, Terry Lyons, Yannis Kevrekidis, and Tom Woolf. Benchmarking optimality of time series classification methods in distinguishing diffusions. arXiv2301   PDF  
  2. F.Lu, Changhong Mou, Honghu Liu, and Traian Iliescu. Stochastic Data-Driven Variational Multiscale Reduced Order Models. preprint. arXiv2209   PDF   MATLAB code

Published

  1. Shai Zucker, Xiong Wang, F.Lu, Inbar Seroussi. Minimax Rates for Learning Pairwise Interactions in Attention-Style Models. ICLR, 2026. arXiv2510
  2. Haibo Li, Jinchao Feng, and F.Lu. Scalable iterative data-adaptive RKHS regularization. To appear on SISC. arXiv2401     PDF   MATLAB code
  3. Quanjun Lang, Xiong Wang, F.Lu, and Mauro Maggioni. Interacting Particle Systems on Networks: joint inference of the network and the interaction kernel. Applied and Computational Harmonic Analysis, 101867, 2026. arXiv2402   PDF   MATLAB code     Podcast by Google NotebookLM
  4. Erhan Bayraktar, F.Lu, Mauro Maggioni, Ruoyu Wu, and Sichen Yang. Probabilistic cellular automata with local transition matrices: synchronization, ergodicity, and inference. To appear in Bernoulli Journal. arXiv2405   PDF  
  5. Meng Fang, Xiangpeng Wan, F.Lu, Fei Xing, and Kai Zou. MathOdyssey: Benchmarking Mathematical Problem-Solving Skills in Large Language Models Using Odyssey Math Data. Scientific Data, 12 (1), 1392, 2025. arXiv2406
  6. F.Lu and Miao-Jung Yvonne Ou. An adaptive RKHS regularization for Fredholm integral equations. Mathematical Methods in the Applied Sciences, 48 (11), 11124-11140, 2025. arXiv2303   PDF   MATLAB code
  7. Yue Yu, Ning Liu, F.Lu, Tian Gao, Siavash Jafarzadeh, Stewart Silling. Nonlocal Attention Operator: Materializing Hidden Knowledge Towards Interpretable Physics Discovery. NeurIPS 2024. arXiv2408
  8. Xingjie Li, F.Lu, Molei Tao, Felix X-F Ye. Robust First and Second-Order Differentiation for Regularized Optimal Transport.   SIAM Journal on Scientific Computing (SISC), vol 47, iss. 3, 2025. journal     arXiv2407    
  9. Neil K. Chada, Quanjun Lang, F.Lu, and Xiong Wang. A data-adaptive prior for Bayesian learning of kernels in operators. J. Machine Learning Research, vol. 25, no.317, 1-37, 2024. arXiv2212   PDF  
  10. F.Lu, Qingci An, and Yue Yu. Nonparametric learning of kernels in nonlocal operators. Journal of Peridynamics and Nonlocal Modeling, vol. 6, pp. 347-370, 2024. arXiv2205   PDF
  11. Quanjun Lang and F.Lu. Identifiability of interaction kernels in mean-field equations of interacting particles. Foundations of Data Science (FoDS) 5 (4), 480-502, 2023 arXiv2106   PDF
  12. Zhongyang Li and F.Lu. On the coercivity condition in the learning of interacting particle systems.   Stochastic Dynamics. vol. 23, no. 08, 2340003, 2023. arXiv2011   PDF
  13. Xingjie Li, F.Lu, Molei Tao and Felix Ye. NySALT: Nyström-type inference-based schemes adaptive to large time-stepping.   J. Comput. Phys., vol.477, 111952, 2023. journal arXiv2207   PDF
  14. Qingci An, Yannis Kevrekidis, F.Lu and Mauro Maggioni. Unsupervised learning of observation functions in state-space models by nonparametric moment methods. Foundation of Data Science, vol. 5, iss. 3, pp. 340-365, 2023. journal arXiv2207   PDF
  15. F.Lu, Quanjun Lang and Qingci An. DARTR: Data adaptive RKHS Tikhonov regularization for learning kernels in operators. Mathematical and Scientific Machine Learning, PMLR, 158-172, 2022. arXiv2203   PDF   MATLAB code
  16. Nan Chen, Honghu Liu and F.Lu. Shock trace prediction by reduced models for a viscous stochastic Burgers equation. Chaos, 32(4), 043109, 2022. arXiv2112   PDF
  17. Quanjun Lang and F.Lu. Learning interaction kernels in mean-field equations of 1st-order systems of interacting particles. SIAM Journal on Scientific Computing 44 (1), A260–A285, 2022. arXiv2010   PDF
  18. Xingjie Li, F.Lu and Felix X.F. Ye. ISALT: Inference-based schemes adaptive to large time-stepping for locally Lipschitz ergodic systems. Discrete and Continuous Dynamical Systems - Series S (DCDS-S) 15 (4), 747-771, 2022.   arXiv2102   PDF
  19. F.Lu, Mauro Maggioni and Sui Tang. Learning interaction kernels in stochastic systems of interacting particles from multiple trajectories. Found. Comput. Math., vol. 22, pp.1013–1067, 2021. arXiv2007 Journal   PDF
  20. F.Lu, Mauro Maggioni and Sui Tang: Learning interaction kernels in heterogeneous systems of agents from multiple trajectories. J. Machine Learning Research, vol. 22, no.32, 1-67, 2021. arXiv1910 Journal   PDF
  21. 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   PDF
  22. F.Lu. Data-driven model reduction for stochastic Burgers equations. Entropy, 22(12), 1360, 2020. arXiv2010 Journal   PDF
  23. Zhongyang Li, F.Lu, Mauro Maggioni, Sui Tang and Cheng Zhang: On the identifiability of interaction functions in systems of interacting particles. Stoch.Process.Their Appl. 132, 135-163, 2021. arXiv1912 Journal PDF
  24. Kevin 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
  25. F.Lu, Nils Weitzel and Adam 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
  26. F.Lu, Ming Zhong, Sui Tang and Mauro 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)
  27. F.Lu, Xuemin Tu and Alexandre J. Chorin Accounting for model error from unresolved scales in ensemble Kalman filters by stochastic parametrization. Mon. Wea. Rev., 145, no. 9, 3709--3723, 2017. Journal   PDF
  28. F.Lu, Kevin K. Lin and Alexandre J. Chorin Data-based stochastic model reduction for the Kuramoto--Sivashinsky equation. Physica D, 340, 46--57, 2017. Journal   PDF
  29. F.Lu, Kevin K. Lin and Alexandre J. Chorin Comparison of continuous and discrete-time data-based modeling for hypoelliptic systems. Comm. App. Math. Com. Sc., 11, no. 2, 187--216, 2016. Journal   PDF
  30. Alexandre J. Chorin, F.Lu, R. N. Miller, M. Morzfeld and Xuemin Tu. Sampling, feasibility, and priors in data assimilation. Discrete Contin. Dyn. Syst. Ser. A, 36, no. 8, 4227--4246, 2016. Journal   PDF
  31. Alexandre J. Chorin and F.Lu. Discrete approach to stochastic parametrization and dimension reduction in nonlinear dynamics. Proc. Natl. Acad. Sci. USA, 112, no. 32, 9804--9809, 2015. Journal   PDF
  32. F.Lu, Matthias Morzfeld, Xuemin Tu and Alexandre J. Chorin Limitations of polynomial chaos expansions in the Bayesian solution of inverse problems. J. Comput. Phys. 282, 138--147, 2015. Journal   PDF
  33. Yaozhong Hu, F.Lu and David Nualart. Convergence of Densities of functionals of Gaussian Processes. J. Funct. Anal. 266, no. 2, 814--875, 2014. Journal   PDF
  34. Yaozhong Hu, F.Lu and David Nualart. Non-degeneracy of Sobolev Pseudo-norms of fractional Brownian motions. Electron. Commun. Probab. 18, no.84, 1--8, 2013.Journal   PDF
  35. Yaozhong Hu, F.Lu and David Nualart. Holder continuity of the solution for a class of nonlinear SPDEs arising from one-dimensional superprocesses. Probab. Theory Related Fields 156, no.1-2, 27--49, 2013. Journal   PDF
  36. Yaozhong Hu, F.Lu and David Nualart. Feynman-Kac formula for the heat equation driven by fractional noise with Hurst parameter H<1/2. Ann. Probab. 40, No. 3, 1041--1068, 2012. Journal   PDF
  37. F.Lu. Branching points for a class of variational equations involving potential with parameter. Adv. Nonlinear Stud., vol. 8, no. 2, pp. 251--269, 2008.

Conference papers and other publications

  • F.Lu, Kevin K. Lin, and Alexandre J. Chorin. Data-driven stochastic model reduction. Paper for Advancing X-cutting Ideas for Computational Climate Science, 2016.
  • F.Lu, Malliavin Calculus and its applications to SPDEs. PhD thesis, University of Kansas, 2013.