Concise, accurate descriptions of physical systems through their conserved quantities
abound in the natural sciences. In data science, however, current research often focuses on …

Deep convolutional neural networks (DCNN) have been successfully used in many low-
level vision problems such as image denoising. Recent studies on the mathematical …

We develop a unified model, known as MgNet, that simultaneously recovers some
convolutional neural networks (CNN) for image classification and multigrid (MG) methods for …

This paper proposes a supervised machine learning framework for the non-intrusive model
order reduction of unsteady fluid flows to provide accurate predictions of non-stationary state …

Neural Ordinary Differential Equation (Neural ODE) has been proposed as a continuous
approximation to the ResNet architecture. Some commonly used regularization mechanisms …

It has been observed that residual networks can be viewed as the explicit Euler
discretization of an Ordinary Differential Equation (ODE). This observation motivated the …

We consider recent work of Haber and Ruthotto 2017 and Chang et al. 2018, where deep
learning neural networks have been interpreted as discretisations of an optimal control …

Attempts from different disciplines to provide a fundamental understanding of deep learning
have advanced rapidly in recent years, yet a unified framework remains relatively limited. In …

Purpose Dual‐energy CT (DECT) has been increasingly used in imaging applications
because of its capability for material differentiation. However, material decomposition suffers …

Convolutional neural networks (CNNs) have been shown to achieve optimal approximation
and estimation error rates (in minimax sense) in several function classes. However, previous …