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20182026
most citedConditioning of Random Feature Matrices: Double Descent and Generalization Error

6 citations · 10 across the 21 of their papers we have counts for

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7 papers · 1 filter

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…

math.NA2026

MVNN: A Measure-Valued Neural Network for Learning McKean-Vlasov Dynamics from Particle Data

Liyao Lyu, Xinyue Yu, Hayden Schaeffer

Collective behaviors that emerge from interactions are fundamental to numerous biological systems. To learn such interacting forces from observations, we introduce a measure-valued…

math.NA2025

Finite Element Representation Network (FERN) for Operator Learning with a Localized Trainable Basis

Zecheng Zhang, Hao Liu, Guosheng Fu +2

We propose a finite-element local basis-based operator learning framework for solving partial differential equations (PDEs). Operator learning aims to approximate mappings from inp…

math.NA2023

D2NO: Efficient Handling of Heterogeneous Input Function Spaces with Distributed Deep Neural Operators

Zecheng Zhang, Christian Moya, Lu Lu +2

Neural operators have been applied in various scientific fields, such as solving parametric partial differential equations, dynamical systems with control, and inverse problems. Ho…

math.NA2023

Bayesian deep operator learning for homogenized to fine-scale maps for multiscale PDE

Zecheng Zhang, Christian Moya, Wing Tat Leung +2

We present a new framework for computing fine-scale solutions of multiscale Partial Differential Equations (PDEs) using operator learning tools. Obtaining fine-scale solutions of m…