A Nonlocal Aggregation–Diffusion Model with Adaptive Perception Kernels for Descriptive Norm Dynamics
- 1Faculty of AI Technologies, ITMO University, Saint Petersburg 197101, Russia
Abstract
This paper presents a partial differential equation (PDE)-based auto-aggregation model for simulating descriptive norm dynamics in autonomous multi-agent systems, capturing convergence and violation through nonlocal perception kernels and external potential fields. Extending classical transport equations, the framework represents opinion popularity as a continuous distribution, enabling direct interactions without Bayesian guessing of beliefs. Using azithromycin and prednisolone as illustrative treatment features from a real-world coronavirus disease 2019 (COVID-19) dataset, the numerical experiments exhibit reduced local perception-to-target discrepancy under target-based updating, redistribution and the formation of a new unimodal density under fact-informed updates with potential guidance, and persistent multiple peaks without target-based fitting or an external potential field. Quantitative evaluation uses population-weighted local perception-to-target Wasserstein distance estimates for the selected treatment dimensions.
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BibTeX
@article{li2026nonlocal,
title = {{A Nonlocal Aggregation–Diffusion Model with Adaptive Perception Kernels for Descriptive Norm Dynamics}},
author = {Chao Li and Ilia Derevitskii and Sergey Kovalchuk},
journal = {Mathematics},
year = {2026},
month = oct,
doi = {10.3390/math14203837},
url = {https://www.mdpi.com/2227-7390/14/20/3837},
note = {CC BY 4.0},
}
RIS
TY - JOUR
TI - A Nonlocal Aggregation–Diffusion Model with Adaptive Perception Kernels for Descriptive Norm Dynamics
AU - Chao Li
AU - Ilia Derevitskii
AU - Sergey Kovalchuk
PY - 2026
DA - 2026/10/21
JO - Mathematics
DO - 10.3390/math14203837
UR - https://www.mdpi.com/2227-7390/14/20/3837
AB - This paper presents a partial differential equation (PDE)-based auto-aggregation model for simulating descriptive norm dynamics in autonomous multi-agent systems, capturing convergence and violation through nonlocal perception kernels and external potential fields. Extending classical transport equations, the framework represents opinion popularity as a continuous distribution, enabling direct interactions without Bayesian guessing of beliefs. Using azithromycin and prednisolone as illustrative treatment features from a real-world coronavirus disease 2019 (COVID-19) dataset, the numerical experiments exhibit reduced local perception-to-target discrepancy under target-based updating, redistribution and the formation of a new unimodal density under fact-informed updates with potential guidance, and persistent multiple peaks without target-based fitting or an external potential field. Quantitative evaluation uses population-weighted local perception-to-target Wasserstein distance estimates for the selected treatment dimensions.
SN - 2227-7390
ER -