4 papers
Resolution-Independent Analysis of Encoder--Decoder Operator Learning via Limiting Kernels
Lei Shi, Jia-Qi Yang, Ding-Xuan Zhou
Operator learning is formulated on function spaces, but training data are typically available only through finite-dimensional representations. In encoder--decoder architectures, a…
Solving PDEs on Spheres with Physics-Informed Convolutional Neural Networks
Guanhang Lei, Zhen Lei, Lei Shi +2
Physics-informed neural networks (PINNs) have been demonstrated to be efficient in solving partial differential equations (PDEs) from a variety of experimental perspectives. Some r…
Classification with Deep Neural Networks and Logistic Loss
Zihan Zhang, Lei Shi, Ding-Xuan Zhou
Deep neural networks (DNNs) trained with the logistic loss (i.e., the cross entropy loss) have made impressive advancements in various binary classification tasks. However, general…
Capacity dependent analysis for functional online learning algorithms
Xin Guo, Zheng-Chu Guo, Lei Shi
This article provides convergence analysis of online stochastic gradient descent algorithms for functional linear models. Adopting the characterizations of the slope function regul…