Abstract Aiming to improve the model’s generalization performance for nonlinear system modeling, a self-organizing reciprocal modular neural network (SORMNN) is proposed in the present study, which imitates the modular structure with inter-module connections observed in human brains. The inter-module connections in SORMNN are built by inputting the output of each subnetwork to other subnetworks. All subnetworks work in parallel to process the allocated features, and the structure of each subnetwork is designed to be self-organized by using a growing and pruning algorithm based on the contribution of hidden neurons. An improved Levenberg-Marquardt (LM) algorithm using a sliding window is conducted to update the parameters of SORMNN, which makes SORMNN available for solving online problems. To validate the effectiveness of the proposed model, SORMNN is tested on chaotic benchmark time series prediction, four UCI benchmark problems and a practical problem for biochemical oxygen demand prediction in wastewater treatment process. Experimental results demonstrate that SORMNN exhibits both a higher training accuracy and a better generalization ability for nonlinear system modeling than other modular neural networks, and the inter-module connections have a positive effect on the superior performance of the proposed model and can make the network structure compact.

中文翻译：

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非线性系统建模的自组织互易模神经网络设计

摘要 为了提高模型对非线性系统建模的泛化性能，本研究提出了一种自组织互易模块化神经网络（SORMNN），它模仿在人脑中观察到的具有模块间连接的模块化结构。SORMNN 中的模块间连接是通过将每个子网络的输出输入到其他子网络来构建的。所有子网络并行工作以处理分配的特征，每个子网络的结构设计为通过使用基于隐藏神经元贡献的增长和修剪算法自组织。采用滑动窗口的改进Levenberg-Marquardt (LM)算法更新SORMNN的参数，使SORMNN可用于解决在线问题。为了验证所提出模型的有效性，SORMNN 在混沌基准时间序列预测、四个 UCI 基准问题和废水处理过程中生化需氧量预测的一个实际问题上进行了测试。实验结果表明，与其他模块化神经网络相比，SORMNN 对非线性系统建模具有更高的训练精度和更好的泛化能力，并且模块间连接对所提出模型的优越性能有积极的影响，可以使网络结构袖珍的。