Neural networks have become a widely adopted tool for modeling nonlinear dynamical systems from data. However, the choice of training strategy remains a key design decision, particularly for simulation tasks. This paper compares two predominant strategies: parallel and series-parallel training. The conducted empirical analysis spans five neural network architectures and two examples: a pneumatic valve test bench and an industrial robot benchmark. The study reveals that, even though series-parallel training dominates current practice, parallel training consistently yields better long-term prediction accuracy. Additionally, this work clarifies the often inconsistent terminology in the literature and relate both strategies to concepts from system identification. The findings suggest that parallel training should be considered the default training strategy for neural network-based simulation of dynamical systems.

翻译：神经网络已成为从数据中建模非线性动力学系统的广泛采用工具。然而，训练策略的选择仍是一个关键设计决策，尤其在仿真任务中。本文比较了两种主要策略：并行训练与串并行训练。所进行的实证分析涵盖五种神经网络架构和两个示例：一个气动阀门测试台和一个工业机器人基准。研究表明，尽管串并行训练在当前实践中占主导地位，但并行训练始终能提供更好的长期预测精度。此外，本研究澄清了文献中常不一致的术语，并将两种策略与系统辨识中的概念联系起来。研究结果表明，对于基于神经网络的动力学系统仿真，并行训练应被视为默认训练策略。