Learning differential equations from data
This work addresses the challenge of data-driven modeling for differential equations in fields like physics and engineering, but it appears incremental as it builds on existing neural network approaches.
The authors tackled the problem of learning differential equations from data by proposing a forward-Euler based neural network model, and they tested its performance on ODEs like the FitzHugh-Nagumo equations with varying hidden layers and widths, but no concrete numerical results were provided.
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.