Multiscale is a hallmark feature of complex nonlinear systems. While the
simulation using the classical numerical methods is restricted by the local
\textit{Taylor} series constraints, the multiscale techniques are often limited
by finding heuristic closures. This study proposes a new method for simulating
multiscale problems using deep neural networks. By leveraging the hierarchical
learning of neural network time steppers, the method adapts time steps to
approximate dynamical system flow maps across timescales. This approach
achieves state-of-the-art performance in less computational time compared to
fixed-step neural network solvers. The proposed method is demonstrated on
several nonlinear dynamical systems, and source codes are provided for
implementation. This method has the potential to benefit multiscale analysis of
complex systems and encourage further investigation in this area.

使用深度神经网络模拟多尺度问题的新方法，通过利用神经网络时间步进器的分层学习，自适应时间步长以近似不同时间尺度上的动力学系统流动图，与固定步长神经网络求解器相比，该方法在较少的计算时间内实现了业界领先的性能。