Using Artificial Neural Networks (ANN) for nonlinear system identification has proven to be a promising approach, but despite of all recent research efforts, many practical and theoretical problems still remain open. Specifically, noise handling and models, issues of consistency and reliable estimation under minimisation of the prediction error are the most severe problems. The latter comes with numerous practical challenges such as explosion of the computational cost in terms of the number of data samples and the occurrence of instabilities during optimization. In this paper, we aim to overcome these issues by proposing a method which uses a truncated prediction loss and a subspace encoder for state estimation. The truncated prediction loss is computed by selecting multiple truncated subsections from the time series and computing the average prediction loss. To obtain a computationally efficient estimation method that minimizes the truncated prediction loss, a subspace encoder represented by an artificial neural network is introduced. This encoder aims to approximate the state reconstructability map of the estimated model to provide an initial state for each truncated subsection given past inputs and outputs. By theoretical analysis, we show that, under mild conditions, the proposed method is locally consistent, increases optimization stability, and achieves increased data efficiency by allowing for overlap between the subsections. Lastly, we provide practical insights and user guidelines employing a numerical example and state-of-the-art benchmark results.

翻译：利用人工神经网络进行非线性系统辨识已被证明是一种有前景的方法，但尽管近年来研究投入众多，许多实际和理论问题仍然悬而未决。具体而言，噪声处理与建模、一致性保证以及在预测误差极小化下的可靠估计是最严峻的问题。后者伴随着诸多实践挑战，例如计算成本随数据样本数量呈爆炸式增长以及优化过程中出现不稳定性。本文旨在克服这些难题，提出一种基于截断预测损失与子空间编码器进行状态估计的方法。截断预测损失通过从时间序列中选取多个截断子段并计算平均预测损失得到。为实现计算高效且能极小化截断预测损失的估计方法，引入了由人工神经网络表示的子空间编码器。该编码器旨在逼近估计模型的状态重构映射，从而根据历史输入与输出为每个截断子段提供初始状态。通过理论分析，我们证明在温和条件下，所提方法具有局部一致性，可提升优化稳定性，并允许子段间重叠以提高数据利用效率。最后，通过数值算例及前沿基准测试结果，提供了实践见解与使用指南。