# Continuous Convolutional Neural Networks: Coupled Neural PDE and ODE

arXiv: https://arxiv.org/abs/2111.00343 · HTML: https://mlsanity.com/paper/2111.00343/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 2 of its 5 references that are in the map.
- First posted on arXiv 30 Oct 2021.

## Builds on (most cited first, 2 of 2)

- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Phased LSTM: Accelerating Recurrent Network Training for Long or Event-based Sequences](https://mlsanity.com/paper/1610.09513/) (2016)

## Abstract (arXiv)

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.