Interacting particle systems, also known as agent-based models (ABMs), represent one category of dynamical systems that are used to study a wide range of physical phenomena across multiple scales. Examples from science and engineering include cell migration, swarm robotics, social psychology, and animal migration patterns and interactions. A ubiquitous feature of such systems is that they exhibit a form of emergence: local interactions leading to large-scale coordination. A fundamental scientific question is thus to understand the local interactions that give rise to the observed emergent dynamics. We are interested in methods for learning interactions generally, which can describe any ABM defined by an interaction kernel without making any additional assumptions about the analytical form of this kernel (i.e. it is non-parametric). The advantage of this kernel-based approach is that it incorporates the underlying physics of the model (i.e. collective dynamics), which more general approaches may ignore, potentially limiting their effectiveness. We propose to extend a non-parametric statistical learning approach for learning the interaction kernel for systems with both self-propulsion and collective dynamics, given an observed set of trajectories. First, we parametrically learn the intra-agent force while simultaneously inferring the interaction kernel non-parametrically. The method is validated on two well-known models. We extended this approach to learn the intra-agent force non-parametrically. Also, we explored how to identify the best-fit model among all possible variations for learning interacting particle collective motion based on observations.. Also, we will introduce an alternative neural network framework to the existing non-parametric statistical learning approach.
