Supervised operator learning centers on the use of training data, in the form of input-output
pairs, to estimate maps between infinite-dimensional spaces. It is emerging as a powerful …

Operator learning trains a neural network to map functions to functions. An ideal operator
learning framework should be mesh-free in the sense that the training does not require a …

This paper provides a comprehensive error analysis of learning with vector-valued random
features (RF). The theory is developed for RF ridge regression in a fully general infinite …

Sparse random mode decomposition (SRMD) is a decomposition approach established by
combining sparse random feature model with clustering algorithm. It is not subject to the …

We introduce a general framework for active learning in regression problems. Our
framework extends the standard setup by allowing for general types of data, rather than …

Operator learning trains a neural network to map functions to functions. An ideal operator
learning framework should be mesh-free in the sense that the training does not require a …

Sparse random mode decomposition (SRMD) is an emerging signal decomposition method
for analyzing time series data. However, SRMD is unable to adaptively select suitable …

Particle dynamics and multi-agent systems provide accurate dynamical models for studying
and forecasting the behaviour of complex interacting systems. They often take the form of a …

The modeling and processing of vectorial electromagnetic (EM) waves in inhomogeneous
media are important problems in physics and engineering, and new methods need to be …

This work considers the fundamental problem of learning an unknown object from training
data using a given model class. We introduce a unified framework that allows for objects in …