  This paper focuses on inverse problems arising in studying multi-population
aggregations. The goal is to reconstruct the diffusion coefficient, advection
coefficient, and interaction kernels of the aggregation system, which
characterize the dynamics of different populations. In the theoretical analysis
of the physical setup, it is crucial to ensure non-negativity of solutions. To
address this, we employ the high-order variation method and introduce
modifications to the systems. Additionally, we propose a novel approach called
transformative asymptotic technique that enables the recovery of the diffusion
coefficient preceding the Laplace operator, presenting a pioneering method for
this type of problems. Through these techniques, we offer comprehensive
insights into the unique identifiability aspect of inverse problems associated
with multi-population aggregation models.
