Simultaneous inference of environmental and interaction forces in collective dynamics

This paper addresses the challenge of discovering the governing equations of collective dynamical systems from observed trajectory data. Instead of treating the system as an arbitrary high-dimensional vector field, the authors leverage the known structure of collective dynamics, where large-scale coordination emerges from local pairwise interactions. They extend existing variational learning methods to simultaneously infer both the interaction kernel (which quantifies inter-agent forces) and the environmental force (which accounts for self-propulsion or external influences). The framework offers both a fully non-parametric approach and a semi-parametric approach, the latter of which allows for the inclusion of prior knowledge regarding the functional form of environmental forces.

The proposed methodology is validated across several benchmark models, including synchronization (Kuramoto model), self-propelled particles (SPP), and phototaxis. The authors demonstrate that their approach can accurately recover mechanistic interaction kernels and environmental forces even with limited training data. A key contribution is the introduction of a model-selection procedure that uses the learned models to distinguish between different collective dynamics frameworks. By evaluating candidate models based on their ability to reproduce observed trajectories and their structural complexity, the procedure can automatically identify the most likely mechanistic model, such as distinguishing between alignment-only systems and those involving environmental forcing.

Understanding the mechanistic drivers of collective behavior is essential for fields ranging from biology to swarm robotics. By providing a data-driven way to recover these mechanisms without making strong a priori assumptions, this framework enables researchers to build predictive models that are grounded in physical reality. The ability to scale to larger populations and generalize across different system sizes makes this approach particularly useful for experimental settings where only small-scale trajectory data may be available.