4 papers
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…
Solving Partial Differential Equations with Random Feature Models
Chunyang Liao
Machine learning based partial differential equations (PDEs) solvers have received great attention in recent years. Most progress in this area has been driven by deep neural networ…
Cauchy Random Features for Operator Learning in Sobolev Space
Chunyang Liao, Deanna Needell, Hayden Schaeffer
Operator learning is the approximation of operators between infinite dimensional Banach spaces using machine learning approaches. While most progress in this area has been driven b…
Differentially Private Random Feature Model
Chunyang Liao, Deanna Needell, Hayden Schaeffer +1
Designing privacy-preserving machine learning algorithms has received great attention in recent years, especially in the setting when the data contains sensitive information. Diffe…