We introduce the framework of continuous-depth graph neural networks (GNNs). Graph neural ordinary differential equations (GDEs) are formalized as the counterpart to GNNs where the input-output ...

It is illustrated by examples and graphs of functions, with each chapter containing exercises solved in the last chapter. Sample Chapter(s) Chapter 1: Introduction (331 KB) ... This chapter presents ...

Linear functions are used to model a broad range of real-world problems. The ability to solve linear equations and inequalities is an essential skill for analysing these models. This section covers ...

Multivariate time series prediction has aroused widely research interests during decades. However, the spatial heterogeneity and temporal evolution characteristics bring much challenges for ...

Graph Convolution Networks (GCNs) are widely considered state-of-the-art for collaborative filtering. Although several GCN-based methods have been proposed and achieved state-of-the-art performance in ...

Backward Stochastic Differential Equations (BSDEs) constitute a class of stochastic processes where the solution is determined by a prescribed terminal condition rather than an initial one.

We propose Graph Neural ODE++, an improved paradigm for Graph Neural Ordinary Differential Equations (GDEs). Inspired by recent literature in score-based generative models, we explore two different ...

Linear Differential Equations in ... Hermite and Legendre orthonormal polynomials and recursive methods for their calculus, with their graphs. The conditions for the convergence of the expansions of ...

The graphs for the pair of simultaneous equations intersect at \(\left(\dfrac{43}{13},\dfrac{85}{26}\right)\). Solving simultaneous equations with an unknown coefficient, \(k\) Questions that include ...