Seminario EDP UAM-ICMAT
Nonlocal interaction kernels inference in nonlinear gradient flow equations
Ponente: Gissell Estrada-Rodriguez (UPC)Fecha: viernes 07 de marzo de 2025 - 11:00Lugar: Aula 520, Módulo 17, Departamento de Matemáticas, UAM
Resumen:
When applying nonlinear aggregation-diffusion equations to model real life phenomenon, a major challenge lies on the choice of the interaction potential. Previous numerical and theoretical studies typically required predetermination of terms and the goal is often to reproduce the observed dynamics qualitatively, not quantitatively. In this talk, we address the inverse problem of identifying nonlocal interaction potentials in nonlinear aggregation-diffusion equations from noisy discrete trajectory data. Our approach involves formulating and solving a regularised variational problem, which requires minimising a quadratic error functional across a set of hypothesis functions. A key theoretical contribution is our novel stability estimate for the PDE, validating the error functional ability in controlling the 2-Wasserstein distance between solutions generated using the true and estimated interaction potentials. We demonstrate the effectiveness of the methods through various 1D and 2D examples showcasing collective behaviours.
Reference: J. A. Carrillo, G. Estrada-Rodriguez, L. Mikolas, and S. Tang, Sparse identification
of nonlocal interaction kernels in nonlinear gradient flow equations via partial inversion. To appear
M3AS, 2025.
