4 papers
Efficient Approximation for Encoder--Decoder Neural Operators via Variation Spaces
Jia-Qi Yang, Lei Shi
We study operator learning using encoder--decoder neural networks. Inspired by the function-space theory of neural networks, we introduce a variation space as an infinite-dimension…
Learning Operators by Regularized Stochastic Gradient Descent with Operator-valued Kernels
Jia-Qi Yang, Lei Shi
We consider a class of statistical inverse problems involving the estimation of a regression operator from a Polish space to a separable Hilbert space, where the target lies in a v…
A Kernel-based Stochastic Approximation Framework for Nonlinear Operator Learning
Jia-Qi Yang, Lei Shi
We develop a stochastic approximation framework for learning nonlinear operators between infinite-dimensional spaces utilizing general Mercer operator-valued kernels. Our framework…
Learning Operators with Stochastic Gradient Descent in General Hilbert Spaces
Lei Shi, Jia-Qi Yang
This study investigates leveraging stochastic gradient descent (SGD) to learn operators between general Hilbert spaces. We propose weak and strong regularity conditions for the tar…