A full-fledged neural network modeling, based on a Multi-layered Nonlinear Autoregressive Exogenous Neural Network (NARX) architecture, is proposed for quasi-static and dynamic hysteresis loops, one of the most challenging topics for computational magnetism. This modeling approach overcomes drawbacks in attaining better than percent-level accuracy of classical and recent approaches for accelerator magnets, that combine hybridization of standard hysteretic models and neural network architectures. By means of an incremental procedure, different Deep Neural Network Architectures are selected, fine-tuned and tested in order to predict magnetic hysteresis in the context of electromagnets. Tests and results show that the proposed NARX architecture best fits the measured magnetic field behavior of a reference quadrupole at CERN. In particular, the proposed modeling framework leads to a percent error below 0.02% for the magnetic field prediction, thus outperforming state of the art approaches and paving a very promising way for future real time applications.

中文翻译：

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基于多层 NARX 神经网络方法的以铁为主的磁体磁滞建模

一个成熟的神经网络建模，基于多层非线性自回归外生神经网络（NARX）架构，被提出用于准静态和动态磁滞回线，这是计算磁学中最具挑战性的主题之一。这种建模方法克服了在获得优于经典和最近加速器磁体方法的百分比精度方面的缺点，这些方法结合了标准滞后模型和神经网络架构的混合。通过增量过程，选择、微调和测试不同的深度神经网络架构，以预测电磁体环境中的磁滞。测试和结果表明，所提出的 NARX 架构最适合在 CERN 测量的参考四极杆的磁场行为。特别是，所提出的建模框架导致磁场预测的百分比误差低于 0.02%，