Continuous Convolutional Neural Networks: Coupled Neural PDE and ODE

• URL: http://arxiv.org/abs/2111.00343v1
• Date: Sat, 30 Oct 2021 21:45:00 GMT
• Title: Continuous Convolutional Neural Networks: Coupled Neural PDE and ODE
• Authors: Mansura Habiba, Barak A. Pearlmutter
• Abstract summary: This work proposes a variant of Convolutional Neural Networks (CNNs) that can learn the hidden dynamics of a physical system. 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)
• Score: 1.1897857181479061
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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