Continuous Convolutional Neural Networks: Coupled Neural PDE and ODE
Abstract
Recent work in deep learning focuses on solving physical systems in the Ordinary Differential Equation or Partial Differential Equation. This current work proposed a variant of Convolutional Neural Networks (CNNs) that can learn the hidden dynamics of a physical system using ordinary differential equation (ODEs) systems (ODEs) and Partial Differential Equation systems (PDEs). Instead of considering the physical system such as image, time -series as a system of multiple layers, this new technique can model a system in the form of Differential Equation (DEs). The proposed method has been assessed by solving several steady-state PDEs on irregular domains, including heat equations, Navier-Stokes equations.
Cite
@article{arxiv.2111.00343,
title = {Continuous Convolutional Neural Networks: Coupled Neural PDE and ODE},
author = {Mansura Habiba and Barak A. Pearlmutter},
journal= {arXiv preprint arXiv:2111.00343},
year = {2021}
}
Comments
Proc. of the International Conference on Electrical, Computer and Energy Technologies (ICECET)