We present a data-driven numerical approach for modeling unknown dynamical systems with missing/hidden parameters. The method is based on training a deep neural network (DNN) model for the unknown system using its trajectory data. A key feature is that the unknown dynamical system contains system parameters that are completely hidden, in the sense that no information about the parameters is available through either the measurement trajectory data or our prior knowledge of the system. We demonstrate that by training a DNN using the trajectory data with sufficient time history, the resulting DNN model can accurately model the unknown dynamical system. For new initial conditions associated with new, and unknown, system parameters, the DNN model can produce accurate system predictions over longer time.
翻译:我们提出了一个数据驱动数字方法,用于模拟具有缺失/隐藏参数的未知动态系统,该方法基于利用轨迹数据培训未知系统深神经网络模型(DNN),一个关键特征是未知动态系统包含完全隐藏的系统参数,即没有通过测量轨迹数据或我们先前对系统的知识获得有关参数的信息。我们证明,通过利用具有足够时间历史的轨迹数据培训DNN,由此形成的DNN模型可以准确模拟未知动态系统。对于与新的和未知的系统参数相关的新初始条件,DNN模型可以产生较长时间的准确系统预测。