Vectorized Adjoint Sensitivity Method for Graph Convolutional Neural Ordinary Differential Equations

09/14/2022
by   Jack Cai, et al.
13

This document, as the title stated, is meant to provide a vectorized implementation of adjoint dynamics calculation for Graph Convolutional Neural Ordinary Differential Equations (GCDE). The adjoint sensitivity method is the gradient approximation method for neural ODEs that replaces the back propagation. When implemented on libraries such as PyTorch or Tensorflow, the adjoint can be calculated by autograd functions without the need for a hand-derived formula. In applications such as edge computing and in memristor crossbars, however, autograds are not available, and therefore we need a vectorized derivation of adjoint dynamics to efficiently map the system on hardware. This document will go over the basics, then move on to derive the vectorized adjoint dynamics for GCDE.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
11/25/2017

Efficiently and easily integrating differential equations with JiTCODE, JiTCDDE, and JiTCSDE

We present a family of Python modules for the numerical integration of o...
research
01/05/2020

Scalable Gradients for Stochastic Differential Equations

The adjoint sensitivity method scalably computes gradients of solutions ...
research
09/02/2020

Inverse modified differential equations for discovery of dynamics

We introduce inverse modified differential equations (IMDEs) to contribu...
research
08/23/2023

Graph Neural Stochastic Differential Equations

We present a novel model Graph Neural Stochastic Differential Equations ...
research
12/27/2018

The Wynn identity as the long sought criterion for the choice of the optimal Padé approximant

The performed numerical analysis reveals that Wynn's identity for the co...
research
10/23/2019

Sensitivity-based Heuristic for Guaranteed Global Optimization with Nonlinear Ordinary Differential Equations

We focus on interval algorithms for computing guaranteed enclosures of t...
research
11/26/2021

Asian Giant Hornet Control based on Image Processing and Biological Dispersal

The Asian giant hornet (AGH) appeared in Washington State appears to hav...

Please sign up or login with your details

Forgot password? Click here to reset