论文标题
通过内部复发从粗略的观察中学习精细的尺度动力学
Learning Fine Scale Dynamics from Coarse Observations via Inner Recurrence
论文作者
论文摘要
最近的工作集中在通过深度神经网络（DNN）的数据驱动的学习对数据驱动的学习，目的是对未知系统的动力学进行长期预测。在许多实际应用程序中，由于数据采集过程中的各种限制，通常以时间量表比所需的时间尺度收集来自时间依赖系统的数据。因此，观察到的动力学可能会严重采样，并且不能反映基础系统的真实动力学。本文提出了一种计算技术，可以从这种粗糙观察到的数据中学习精细的动力学。该方法采用DNN的内部复发来恢复基础系统的细尺度进化算子。除了数学上的理由外，还提出了几个具有挑战性的数值示例，包括普通和部分微分方程的未知系统，以证明所提出的方法的有效性。
Recent work has focused on data-driven learning of the evolution of unknown systems via deep neural networks (DNNs), with the goal of conducting long term prediction of the dynamics of the unknown system. In many real-world applications, data from time-dependent systems are often collected on a time scale that is coarser than desired, due to various restrictions during the data acquisition process. Consequently, the observed dynamics can be severely under-sampled and do not reflect the true dynamics of the underlying system. This paper presents a computational technique to learn the fine-scale dynamics from such coarsely observed data. The method employs inner recurrence of a DNN to recover the fine-scale evolution operator of the underlying system. In addition to mathematical justification, several challenging numerical examples, including unknown systems of both ordinary and partial differential equations, are presented to demonstrate the effectiveness of the proposed method.
