Unified Learning of the Profile Function in Discrete Keller-Segel Models

Fuente: arXiv
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Main Authors: Chen, Chi-An, Liu, Chun, Zhong, Ming
Format: Preprint
Published: 2025
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author Chen, Chi-An
Liu, Chun
Zhong, Ming
author_facet Chen, Chi-An
Liu, Chun
Zhong, Ming
contents We propose a unified learning framework for identifying the profile function in discrete Keller-Segel equations, which are widely used mathematical models for understanding chemotaxis. Training data are obtained via either a rigorously developed particle method designed for stable simulation of high-dimensional Keller-Segel systems, or stochastic differential equations approximating the continuous Keller-Segel PDE. Our approach addresses key challenges, including data instability in dimensions higher than two and the accurate capture of singular behavior in the profile function. Additionally, we introduce an adaptive learning strategy to enhance performance. Extensive numerical experiments are presented to validate the effectiveness of our method.
format Preprint
id arxiv_https___arxiv_org_abs_2510_23381
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Unified Learning of the Profile Function in Discrete Keller-Segel Models
Chen, Chi-An
Liu, Chun
Zhong, Ming
Numerical Analysis
We propose a unified learning framework for identifying the profile function in discrete Keller-Segel equations, which are widely used mathematical models for understanding chemotaxis. Training data are obtained via either a rigorously developed particle method designed for stable simulation of high-dimensional Keller-Segel systems, or stochastic differential equations approximating the continuous Keller-Segel PDE. Our approach addresses key challenges, including data instability in dimensions higher than two and the accurate capture of singular behavior in the profile function. Additionally, we introduce an adaptive learning strategy to enhance performance. Extensive numerical experiments are presented to validate the effectiveness of our method.
title Unified Learning of the Profile Function in Discrete Keller-Segel Models
topic Numerical Analysis
url https://arxiv.org/abs/2510.23381