115 citations · 519 across the 28 of their papers we have counts for
28 papers
Small noise analysis for Tikhonov and RKHS regularizations
Quanjun Lang, Fei Lu
Regularization plays a pivotal role in ill-posed machine learning and inverse problems. However, the fundamental comparative analysis of various regularization norms remains open.…
An adaptive RKHS regularization for Fredholm integral equations
Fei Lu, Miao-Jung Yvonne Ou
Regularization is a long-standing challenge for ill-posed linear inverse problems, and a prototype is the Fredholm integral equation of the first kind with additive Gaussian measur…
Stochastic Data-Driven Variational Multiscale Reduced Order Models
Fei Lu, Changhong Mou, Honghu Liu +1
Trajectory-wise data-driven reduced order models (ROMs) tend to be sensitive to training data, and thus lack robustness. We propose to construct a robust stochastic ROM closure (S-…
NySALT: Nyström-type inference-based schemes adaptive to large time-stepping
Xingjie Li, Fei Lu, Molei Tao +1
Large time-stepping is important for efficient long-time simulations of deterministic and stochastic Hamiltonian dynamical systems. Conventional structure-preserving integrators, w…
Unsupervised learning of observation functions in state-space models by nonparametric moment methods
Qingci An, Yannis Kevrekidis, Fei Lu +1
We investigate the unsupervised learning of non-invertible observation functions in nonlinear state-space models. Assuming abundant data of the observation process along with the d…
Nonparametric learning of kernels in nonlocal operators
Fei Lu, Qingci An, Yue Yu
Nonlocal operators with integral kernels have become a popular tool for designing solution maps between function spaces, due to their efficiency in representing long-range dependen…