论文标题
用隐藏参数建模未知的动态系统
Modeling unknown dynamical systems with hidden parameters
论文作者
论文摘要
我们提出了一种数据驱动的数值方法，用于建模具有缺失/隐藏参数的未知动态系统。该方法基于使用其轨迹数据训练未知系统的深神经网络（DNN）模型。一个关键功能是，未知的动态系统包含完全隐藏的系统参数，从某种意义上说，关于参数的信息无法通过测量轨迹数据或我们对系统的先验知识获得。我们证明，通过使用具有足够时间历史的轨迹数据训练DNN，所得的DNN模型可以准确地对未知的动态系统进行建模。对于与新的和未知的系统参数相关的新初始条件，DNN模型可以在更长的时间内产生准确的系统预测。
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.
