15 Apr 2024 | Yuhan Li*, Hongyu Liu†, and Catharine W. K. Lo‡
This paper investigates inverse problems in multi-population aggregation models, focusing on reconstructing diffusion coefficients, advection coefficients, and interaction kernels that characterize population dynamics. The study addresses the challenge of ensuring non-negativity of solutions in these models, employing the high-order variation method and a novel transformative asymptotic technique. These methods enable the recovery of diffusion coefficients and interaction kernels, providing insights into the unique identifiability of inverse problems in multi-population aggregation models.
The paper discusses the mathematical models used to describe self-organizing behaviors in biological systems, including non-local advection-diffusion equations. These equations incorporate both advection and diffusion, allowing for the modeling of long-range interactions and memory effects. The study considers multi-species models that account for interactions between different populations, enabling the analysis of complex dynamics and interactions.
Inverse problems in these models involve determining unknown coefficients from measurement data. The paper presents results showing that under certain conditions, the diffusion coefficients and interaction kernels can be uniquely identified. The study also addresses the unique identifiability of advection coefficients and interaction kernels, demonstrating that these parameters can be recovered from measurement data.
The paper introduces the transformative asymptotic technique, a novel method for solving inverse problems in multi-population aggregation models. This technique allows for the recovery of diffusion coefficients and interaction kernels, providing a new approach to these inverse problems. The study also highlights the importance of non-negativity in biological models, ensuring that solutions remain physically meaningful.
The paper concludes with the main results of the study, demonstrating that under generic conditions, the diffusion coefficients can be uniquely recovered from measurement data. Additionally, the advection coefficients and interaction kernels can be uniquely identified, providing valuable insights into the dynamics of multi-population aggregation models. The study contributes to the understanding of inverse problems in biological systems, offering new methods and insights into the unique identifiability of these models.This paper investigates inverse problems in multi-population aggregation models, focusing on reconstructing diffusion coefficients, advection coefficients, and interaction kernels that characterize population dynamics. The study addresses the challenge of ensuring non-negativity of solutions in these models, employing the high-order variation method and a novel transformative asymptotic technique. These methods enable the recovery of diffusion coefficients and interaction kernels, providing insights into the unique identifiability of inverse problems in multi-population aggregation models.
The paper discusses the mathematical models used to describe self-organizing behaviors in biological systems, including non-local advection-diffusion equations. These equations incorporate both advection and diffusion, allowing for the modeling of long-range interactions and memory effects. The study considers multi-species models that account for interactions between different populations, enabling the analysis of complex dynamics and interactions.
Inverse problems in these models involve determining unknown coefficients from measurement data. The paper presents results showing that under certain conditions, the diffusion coefficients and interaction kernels can be uniquely identified. The study also addresses the unique identifiability of advection coefficients and interaction kernels, demonstrating that these parameters can be recovered from measurement data.
The paper introduces the transformative asymptotic technique, a novel method for solving inverse problems in multi-population aggregation models. This technique allows for the recovery of diffusion coefficients and interaction kernels, providing a new approach to these inverse problems. The study also highlights the importance of non-negativity in biological models, ensuring that solutions remain physically meaningful.
The paper concludes with the main results of the study, demonstrating that under generic conditions, the diffusion coefficients can be uniquely recovered from measurement data. Additionally, the advection coefficients and interaction kernels can be uniquely identified, providing valuable insights into the dynamics of multi-population aggregation models. The study contributes to the understanding of inverse problems in biological systems, offering new methods and insights into the unique identifiability of these models.