3 papers
math.NA2026
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…
math.NA2026
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…
cs.LG2025
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-…