Active Learning Algorithm Using Neural Operator Networks and Bayesian Neural Networks:Learning Macroscale Models for Collective Behavior from Microscale Data
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.
mathematical modelingnonlocal Euler equationsBayesian neural networksactive learning algorithmCucker-Smale model
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