Learning differential equations from data

TL;DR

This paper introduces a neural network approach based on the forward Euler method to learn ordinary differential equations from data, demonstrating its effectiveness on models like FitzHugh-Nagumo.

Contribution

It proposes a novel neural network model inspired by the forward Euler method for data-driven learning of differential equations.

Findings

Effective learning of ODEs like FitzHugh-Nagumo from data

Performance varies with network depth and width

Neural network approach outperforms traditional methods

Abstract

Differential equations are used to model problems that originate in disciplines such as physics, biology, chemistry, and engineering. In recent times, due to the abundance of data, there is an active search for data-driven methods to learn Differential equation models from data. However, many numerical methods often fall short. Advancements in neural networks and deep learning, have motivated a shift towards data-driven deep learning methods of learning differential equations from data. In this work, we propose a forward-Euler based neural network model and test its performance by learning ODEs such as the FitzHugh-Nagumo equations from data using different number of hidden layers and different neural network width.