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.

翻译：多尺度是复杂非线性系统的标志性特征。经典数值方法进行的模拟受限于局部泰勒级数约束，而多尺度技术常因需寻找启发式闭合条件而受限。本研究提出一种利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层次化学习，该方法自适应调整时间步长以逼近跨时间尺度的动力系统流映射。与固定步长神经网络求解器相比，该方法在更短的计算时间内实现了最先进的性能。通过多个非线性动力系统对所提方法进行了验证，并提供了实现源代码。该方法有望为复杂系统的多尺度分析提供助益，并促进该领域的进一步探索。