1 citations · 1 across the 12 of their papers we have counts for
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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…
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…
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 sa…
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…
VICON: Vision In-Context Operator Networks for Multi-Physics Fluid Dynamics Prediction
Yadi Cao, Yuxuan Liu, Liu Yang +3
In-Context Operator Networks (ICONs) have demonstrated the ability to learn operators across diverse partial differential equations using few-shot, in-context learning. However, ex…