6 citations · 11 across the 27 of their papers we have counts for
22 papers · 1 filter
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…
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…
Generalization Bounds and Statistical Guarantees for Multi-Task and Multiple Operator Learning with MNO Networks
Adrien Weihs, Hayden Schaeffer
Multiple operator learning concerns learning operator families indexed by an operator descriptor . Training data are collected hierarchically by sampl…
Adam Improves Muon: Adaptive Moment Estimation with Orthogonalized Momentum
Minxin Zhang, Yuxuan Liu, Hayden Schaeffer
Efficient stochastic optimization typically integrates an update direction that performs well in the deterministic regime with a mechanism adapting to stochastic perturbations. Whi…
PI-MFM: Physics-informed multimodal foundation model for solving partial differential equations
Min Zhu, Jingmin Sun, Zecheng Zhang +2
Partial differential equations (PDEs) govern a wide range of physical systems, and recent multimodal foundation models have shown promise for learning PDE solution operators across…
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-…