Augmented Neural ODEs

04/02/2019
by   Emilien Dupont, et al.
16

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 functions Neural ODEs cannot represent. To address these limitations, we introduce Augmented Neural ODEs which, in addition to being more expressive models, are empirically more stable, generalize better and have a lower computational cost than Neural ODEs.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
07/30/2019

Approximation Capabilities of Neural Ordinary Differential Equations

Neural Ordinary Differential Equations have been recently proposed as an...
research
09/15/2021

Modular Neural Ordinary Differential Equations

The laws of physics have been written in the language of dif-ferential e...
research
08/09/2022

Interpretable Polynomial Neural Ordinary Differential Equations

Neural networks have the ability to serve as universal function approxim...
research
10/28/2020

Parameterized Neural Ordinary Differential Equations: Applications to Computational Physics Problems

This work proposes an extension of neural ordinary differential equation...
research
08/19/2020

Augmenting Neural Differential Equations to Model Unknown Dynamical Systems with Incomplete State Information

Neural Ordinary Differential Equations replace the right-hand side of a ...
research
03/18/2020

Stable Neural Flows

We introduce a provably stable variant of neural ordinary differential e...
research
08/25/2021

Surprisingly Popular Algorithm-based Adaptive Euclidean Distance Topology Learning PSO

The surprisingly popular algorithm (SPA) is a powerful crowd decision mo...

Please sign up or login with your details

Forgot password? Click here to reset