In recent years, tremendous progress has been made on numerical algorithms for solving
partial differential equations (PDEs) in a very high dimension, using ideas from either …

Graph is a natural representation encoding both the features of the data samples and
relationships among them. Analysis with graphs is a classic topic in data mining and many …

Deep learning's performance has been extensively recognized recently. Graph neural
networks (GNNs) are designed to deal with graph-structural data that classical deep …

The turnpike property in contemporary macroeconomics asserts that if an economic planner
seeks to move an economy from one level of capital to another, then the most efficient path …

This paper develops a Pontryagin differentiable programming (PDP) methodology, which
establishes a unified framework to solve a broad class of learning and control tasks. The …

Recent work has attempted to interpret residual networks (ResNets) as one step of a forward
Euler discretization of an ordinary differential equation, focusing mainly on syntactic …

Learning continuous-time dynamics on complex networks is crucial for understanding,
predicting, and controlling complex systems in science and engineering. However, this task …

We compare the discretize-optimize (Disc-Opt) and optimize-discretize (Opt-Disc)
approaches for time-series regression and continuous normalizing flows (CNFs) using …

Over the past few years, deep learning has risen to the foreground as a topic of massive
interest, mainly as a result of successes obtained in solving large-scale image processing …

We represent the optimal control functions by neural networks and solve optimal control
problems by deep learning techniques. Adjoint sensitivity analysis is applied to train the …