Approximating differential equations using neural ODEs.

Differential equations play an important role in modelling all kinds of phenomena in many disciplines. An example is the prey-predator model, also known as the Lotka-Volterra equations. However, sometimes it is the case that there is not enough information known to construct an explicit model for a problem. This study focuses on approximating differential equations using neural ordinary differential equations (neural ODEs), such that data can still be used in models without having to construct an explicit system of ODEs. Neural ODEs are a recent development that combine deep learning with the structure of differential equations. We train our network for various different sets of initial conditions, after which we see how well our network performs during testing on other initial conditions. We do this for the Lotka-Volterra equations and the Van der Pol oscillator. The presented results focus on the performance of the model dependent on the amount of training points and the amount of epochs used during training. We conclude that a neural ODE can make for an accurate approximation of the differential equations, but there are some uncertainties of the influence of the training set and the kind of differential equations that are used for the data set.