Hierarchical deep learning-based adaptive time-stepping scheme for
  multiscale simulations
Asif Hamid Danish Rafiq Shahkar Ahmad Nahvi Mohammad Abid Bazaz
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.