Universal differential equations (UDEs) form a bridge between classical physical modeling and data-driven approaches like machine learning. We will show an application of UDEs for modeling the movement of spherical particles in a carrier fluid. For this purpose, the system of ordinary integro-differential equations known as Maxey-Riley-Gatignol equations is used. They model the movement of small, inertial, spherical particles in a fluid. The integral term in the model makes it difficult to solve this equation using classical numerical methods, which is why it is often neglected in practice. However, since this can lead to qualitatively different solutions and thus to significant deviations even in simple flows, we propose to approximate it by a neural network, trained using reference trajectories. We consider two flow fields: One analytical vortex field and one field that is obtained by interpolating measurement data from a lab-sized stirred tank reactor. We analyze both the deviations of trajectories of individual particles and the clustering patterns of the particles’ final positions. We also compare two different network architectures: A Feedforward Network (FNN) and a long short-term memory (LSTM). The results show that both architectures can replace the integral term and deliver quantitatively and qualitatively accurate approximations to the full model.