对比神经网络训练策略，发现并行训练更适合作为动力系统仿真的默认方法。
Comparison of neural network training strategies for the simulation of dynamical systems
- 采用并行与串行两种训练方式，对比其在动态系统仿真中的表现。
- 并行训练在长期预测上精度始终优于串行训练，尤其在复杂系统中优势明显。
- 澄清了文献中术语混乱问题，适合从事系统建模与控制的研究者参考。
神经网络已成为从数据中建模非线性动力系统的重要工具。然而，训练策略的选择仍是关键设计决策，尤其在仿真任务中。本文比较了两种主流策略：并行训练与串行训练。实验涵盖五种神经网络架构及两个案例：气动阀测试台和工业机器人基准。结果表明，尽管串行训练当前更普遍，但并行训练在长期预测精度上始终更优。此外，本文厘清了文献中术语不一致的问题，并将两种策略与系统辨识理论关联。研究建议，对于基于神经网络的动力系统仿真，应默认采用并行训练策略。
原文摘要 · Abstract (English)
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.
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