Neural ordinary differential equations (ODEs) have been attracting increasing attention in
various research domains recently. There have been some works studying optimization …

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 …

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 …

Deep neural networks have become the state-of-the-art models in numerous machine
learning tasks. However, general guidance to network architecture design is still missing. In …

Democratization of machine learning requires architectures that automatically adapt to new
problems. Neural Differential Equations (NDEs) have emerged as a popular modeling …

Abstract We show that Neural Ordinary Differential Equations (ODEs) learn representations
that preserve the topology of the input space and prove that this implies the existence of …

In deep latent Gaussian models, the latent variable is generated by a time-inhomogeneous
Markov chain, where at each time step we pass the current state through a parametric …

We propose heavy ball neural ordinary differential equations (HBNODEs), leveraging the
continuous limit of the classical momentum accelerated gradient descent, to improve neural …

Abstract Training Neural Ordinary Differential Equations (ODEs) is often computationally
expensive. Indeed, computing the forward pass of such models involves solving an ODE …

We introduce physics informed neural networks--neural networks that are trained to solve
supervised learning tasks while respecting any given law of physics described by general …