Hierarchical deep learning-based adaptive time-stepping scheme for multiscale simulations
This method addresses multiscale simulation bottlenecks for researchers in computational physics and engineering, though it appears incremental as an enhancement to existing neural network solvers.
The paper tackles the challenge of simulating multiscale nonlinear systems by proposing a hierarchical deep learning-based adaptive time-stepping scheme, which achieves state-of-the-art performance with reduced computational time compared to fixed-step neural network solvers.
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.