一类结合神经算子网络与贝叶斯神经网络的主动学习算法:从微观数据学习集群行为的宏观模型
Active Learning Algorithm Using Neural Operator Networks and Bayesian Neural Networks:Learning Macroscale Models for Collective Behavior from Microscale Data
高正雅 1毛志平2
作者信息
- 1. 厦门大学数学科学学院,福建 厦门 361005
- 2. 宁波东方理工大学(暂名)数学科学学院,浙江 宁波 315200
- 折叠
摘要
随着人工智能和科学计算的发展,深度学习在数学建模中发挥着越来越重要的作用.本文发展了一类结合微观数据的主动学习算法对集群行为建立的宏观模型.具体来说,针对 Cucker-Smale 模型,结合微观粒子数据与部分机理,发展了一类结合神经算子网络与贝叶斯神经网络的主动学习算法.该算法可通过群体行为的微观数据高效地建立对应的宏观 Euler模型.最后通过一维和二维数值模拟验证了主动学习算法的有效性.
Abstract
With the development of artificial intelligence and scientific computing,deep learning plays a significant role in mathematical modeling.In this work we develop an active learning algorithm that uses microscopic data to establish a macroscopic model for collective behavior.Specifically,we take the Cucker-Smale model in this work and develop the corresponding active learning algorithm that integrates neural operator networks and Bayesian neural networks by utilizing microscopic particle data and partial physics.This algorithm is used to efficiently establishes the corresponding macroscopic Euler model through microscopic data.Finally,the effectiveness of the active learning algorithm is validated through one-dimensional and two-dimensional numerical simulations.
关键词
数学建模/非局部欧拉方程/贝叶斯神经网络/主动学习算法/Cucker-Smale模型Key words
mathematical modeling/nonlocal Euler equations/Bayesian neural networks/active learning algorithm/Cucker-Smale model引用本文复制引用
出版年
2024
NETL
NSTL
万方数据