4 papers
Loss Curvature as a Sampling-Free Proxy for Memorization in Diffusion Models
Shashank Sule, Xinyue Yu, Boonam Shin +3
Understanding the mechanism behind why diffusion models memorize their training data remains an open question in generative modeling. In this paper, we examine this question from t…
Wasserstein Moment Nudging for Vlasov-Poisson Data Assimilation
Liyao Lyu, Xinyue Yu, David Schneidinger +1
We introduce a continuous data assimilation method for particle-in-cell simulations of the Vlasov-Poisson equation when only hydrodynamic moments are observed. The forecast state i…
Multiscale Nudging: From Macroscopic Observations to Microscopic Dynamics
Liyao Lyu, Xinyue Yu, Hayden Schaeffer
We introduce a measure-based nudging framework for assimilating macroscopic observations into microscopic mean-field particle dynamics. The central difficulty is a representation m…
Regularized Random Fourier Features and Finite Element Reconstruction for Operator Learning in Sobolev Space
Xinyue Yu, Hayden Schaeffer
Operator learning is a data-driven approximation of mappings between infinite-dimensional function spaces, such as the solution operators of partial differential equations. Kernel-…