基于自适应神经网络的PDEs求解研究  

Research on PDEs Solution Based on Adaptive Neural Networks

作　　者：彭杰[1,2] 张玉武 PENG Jie;ZHANG Yuwu(Basic Department of Lu'an Vocational and Technical College,Lu'an Anhui 237158,China;Wuhan University,Wuhan 430072,China)

机构地区：[1]六安职业技术学院基础部,安徽六安237158 [2]武汉大学,湖北武汉430072

出　　处：《佳木斯大学学报（自然科学版）》2024年第3期174-177,共4页Journal of Jiamusi University：Natural Science Edition

基　　金：安徽省教育厅2021年省级安徽省高校优秀拔尖人才培育资助项目(gxgnfx2021194);安徽省高校优秀拔尖人才培育资助项目(gxgnfx2021196)。

摘　　要：针对当前基于神经网络的PDEs求解方法效率和精度均不够理想的缺陷,研究提出一种基于改进BP神经网络(BP neural network,BPNN)的PDEs求解模型。首先,参照自适应网格法来改进神经网络结构,构建自适应神经网络,改进模型的输出精度;其次,提出一种引入Levy飞行机制和鲸鱼优化算法(Whale optimization algorithm,WOA)的改进海鸥优化算法(Improved Seagull Optimization Algorithm,ISOA)来优化BPNN,寻找BPNN的最佳参数,提高模型的性能;基于上述内容,构建基于ISOA-BPNNPDEs智能求解模型。结果显示,该模型的F1值为95.74%,准确率达到97.96%,输出误差为0.021,优于当前最先进的两种PDEs求解模型。上述内容表明,研究构建的基于ISOA-BPNNPDEs智能求解模型能够高效、准确地实现PDEs求解,为PDEs求解研究提供了新的路径。In response to the shortcomings of the current neural network-based PDEs solution method in terms of efficiency and accuracy,a PDEs solution model based on improved BP neural network(BPNN)is proposed.Firstly,refer to the adaptive grid method to improve the neural network structure,construct an adaptive neural network,and improve the output accuracy of the model.Secondly,an Improved Seagull Optimization Algorithm(ISOA)incorporating Levy flight mechanism and Whale Optimization Algorithm(WOA)is proposed to optimize the BPNN,search for the optimal parameters of the BPNN,and improve the performance of the model.Based on the above content,construct an intelligent solution model based on ISOA-BPNNPDEs.The results show that the F1 value of the model is 95.74%,with an accuracy of 97.96%and an output error of 0.021,which is superior to the two most advanced PDEs solving models currently available.The above content indicates that the ISOA-BPNNPDEs intelligent solution model constructed in the study can efficiently and accurately solve PDEs,providing a new path for PDEs solution research.

关 键 词：偏微分方程 神经网络 海鸥优化算法 鲸鱼优化 

分 类 号：O241[理学—计算数学]