Hierarchical deep learning-based adaptive time-stepping scheme for multiscale simulations
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Abstract (arXiv)
Multiscale is a hallmark feature of complex nonlinear systems. While the simulation using the classical numerical methods is restricted by the local textitTaylor 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.
Key facts. Cited by 3 papers in the map (data through 14 Oct 2026). Builds on 18 of its 76 references that are in the map. First posted on arXiv 10 Nov 2023.
Builds on
18 of 76 references.
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6 more
- 2022SeismicNet: Physics-informed neural networks for seismic wave modeling in semi-infinite domaincited by 16
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Citing papers per year: 2024: 1; 2025: 1; 2026: 1.
3 papers.