The SUBNET neural network architecture has been developed to identify nonlinear state-space models from input-output data. To achieve this, it combines the rolled-out nonlinear state-space equations and a state encoder function, both parameterised as neural networks The encoder function is introduced to reconstruct the current state from past input-output data. Hence, it enables the forward simulation of the rolled-out state-space model. While this approach has shown to provide high-accuracy and consistent model estimation, its convergence can be significantly improved by efficient initialization of the training process. This paper focuses on such an initialisation of the subspace encoder approach using the Best Linear Approximation (BLA). Using the BLA provided state-space matrices and its associated reconstructability map, both the state-transition part of the network and the encoder are initialized. The performance of the improved initialisation scheme is evaluated on a Wiener-Hammerstein simulation example and a benchmark dataset. The results show that for a weakly nonlinear system, the proposed initialisation based on the linear reconstructability map results in a faster convergence and a better model quality.

翻译：SUBNET神经网络架构已被开发用于从输入-输出数据中辨识非线性状态空间模型。为实现这一目标，该架构结合了展开形式的非线性状态空间方程和状态编码器函数，两者均参数化为神经网络。引入编码器函数是为了从过去的输入-输出数据中重构当前状态，从而能够对展开的状态空间模型进行前向仿真。尽管该方法已被证明能提供高精度且一致的模型估计，但其收敛性可通过训练过程的高效初始化得到显著改善。本文聚焦于利用最佳线性近似（BLA）对子空间编码器方法进行此类初始化。利用BLA提供的状态空间矩阵及其关联的可重构性映射，对网络的状态转移部分和编码器进行初始化。在维纳-哈默斯坦仿真示例和基准数据集上评估了改进初始化方案的性能。结果表明，对于弱非线性系统，基于线性可重构性映射所提出的初始化能够实现更快的收敛速度和更好的模型质量。