The exploding research interest for neural networks in modeling nonlinear dynamical systems is largely explained by the networks' capacity to model complex input-output relations directly from data. However, they typically need vast training data before they can be put to any good use. The data generation process for dynamical systems can be an expensive endeavor both in terms of time and resources. Active learning addresses this shortcoming by acquiring the most informative data, thereby reducing the need to collect enormous datasets. What makes the current work unique is integrating the deep active learning framework into nonlinear system identification. We formulate a general static deep active learning acquisition problem for nonlinear system identification. This is enabled by exploring system dynamics locally in different regions of the input space to obtain a simulated dataset covering the broader input space. This simulated dataset can be used in a static deep active learning acquisition scheme referred to as global explorations. The global exploration acquires a batch of initial states corresponding to the most informative state-action trajectories according to a batch acquisition function. The local exploration solves an optimal control problem, finding the control trajectory that maximizes some measure of information. After a batch of informative initial states is acquired, a new round of local explorations from the initial states in the batch is conducted to obtain a set of corresponding control trajectories that are to be applied on the system dynamics to get data from the system. Information measures used in the acquisition scheme are derived from the predictive variance of an ensemble of neural networks. The novel method outperforms standard data acquisition methods used for system identification of nonlinear dynamical systems in the case study performed on simulated data.

翻译：神经网络在建模非线性动态系统方面的研究兴趣激增，主要源于其能够直接从数据中学习复杂的输入输出关系。然而，这些网络通常需要海量训练数据才能有效应用。对于动态系统而言，数据生成过程在时间和资源方面可能代价高昂。主动学习通过获取最具信息量的数据来弥补这一不足，从而减少收集庞大数据集的需求。本研究的独特之处在于将深度主动学习框架融入非线性系统辨识。我们针对非线性系统辨识问题，提出了一个通用的静态深度主动学习获取方案。该方案通过在不同输入空间区域局部探索系统动态特性，获得覆盖更广泛输入空间的模拟数据集。该模拟数据集可用于一种称为"全局探索"的静态深度主动学习获取策略：全局探索根据批量获取函数，获取与最具信息量状态-动作轨迹相对应的初始状态批次。局部探索则通过求解最优控制问题，寻找能最大化某种信息度量的控制轨迹。在获取信息量丰富的初始状态批次后，从该批次初始状态出发进行新一轮局部探索，获得一组对应的控制轨迹，将其作用于系统动态特性以获取系统数据。获取方案中使用的信息度量基于神经网络集成模型的预测方差。在基于仿真数据的案例研究中，该新方法优于用于非线性动态系统系统辨识的标准数据获取方法。