1 citations · 1 across the 4 of their papers we have counts for
21 papers
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…
Kernel Methods for Learning Operators with Multiple Inputs and Outputs
Adrien Weihs, Chunyang Liao, Jingmin Sun +1
Learning mappings between infinite-dimensional objects is a central challenge in scientific machine learning. We introduce a general kernel-based encoder-decoder framework for oper…
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…
Neural Scaling Laws of Deep ReLU and Deep Operator Network: A Theoretical Study
Hao Liu, Zecheng Zhang, Wenjing Liao +1
Neural scaling laws play a pivotal role in the performance of deep neural networks and have been observed in a wide range of tasks. However, a complete theoretical framework for un…
Multiple Neural Operators Achieve Near-Optimal Rates for Multi-Task Learning
Adrien Weihs, Hayden Schaeffer
We study the approximation and statistical complexity of learning collections of operators in a shared multi-task setting, with a focus on the Multiple Neural Operators (MNO) archi…
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…