From the 2 of 8 linked papers with an AI index.
8 papers
Dynamical Low-Rank Smoothing
Youssef Marzouk, Fabio Nobile, Fabio Zoccolan
The paper introduces a dynamical low-rank approximation framework to create efficient reduced-order smoothers for high-dimensional stochastic differential equation models, extendin…
Dynamical Low-Rank Filters for Data Assimilation
Yoshihito Kazashi, Youssef Marzouk, Fabio Nobile +1
The paper introduces dynamical low-rank (DLR) filters for data assimilation, deriving methods that jointly minimize mean and covariance errors and extending them to Kalman‑Bucy, en…
Exact affine conditioning beyond Gaussians: a unique characterization of the ensemble Kalman update
Frederic J. N. Jorgensen, Youssef M. Marzouk
The analysis step of the ensemble Kalman filter, called the ensemble Kalman update (EnKU), is widely used for approximating posterior distributions in inverse problems and data ass…
Infinite-Dimensional Diffusion Models
Jakiw Pidstrigach, Youssef Marzouk, Sebastian Reich +1
Diffusion models have had a profound impact on many application areas, including those where data are intrinsically infinite-dimensional, such as images or time series. The standar…
Distributionally Robust Gaussian Process Regression and Bayesian Inverse Problems
Xuhui Zhang, Jose Blanchet, Youssef Marzouk +2
We study a distributionally robust optimization formulation (i.e., a min-max game) for two representative problems in Bayesian nonparametric estimation: Gaussian process regression…
Diffusion map particle systems for generative modeling
Fengyi Li, Youssef Marzouk
We propose a novel diffusion map particle system (DMPS) for generative modeling, based on diffusion maps and Laplacian-adjusted Wasserstein gradient descent (LAWGD). Diffusion maps…