New Method Infers Collective Dynamics Forces Simultaneously

Understanding the local interactions that drive large-scale coordination in collective dynamic systems, such as cell migration or swarm robotics, is a fundamental challenge. Existing methods often make strong assumptions about the analytical form of these interaction kernels. This work introduces a novel approach that avoids such assumptions by using a nonparametric, kernel-based method, which inherently incorporates the underlying physics of collective dynamics. The proposed framework enhances existing variational learning techniques to simultaneously infer both the interaction kernel between agents and the environmental or intra-agent forces acting on them. It employs nonparametric representations for the interaction kernel and offers flexibility with either semi-parametric or fully nonparametric representations for environmental forces. The methodology has been validated across several benchmark models, including those exhibiting synchronization, alignment, and attraction-repulsion behaviors, as well as systems with external environmental forces. Additionally, the research introduces a model-selection procedure to identify optimal models directly from trajectory data.