Corpus ID: 221266564

Hierarchical Deep Learning of Multiscale Differential Equation Time-Steppers

@article{Liu2020HierarchicalDL,
  title={Hierarchical Deep Learning of Multiscale Differential Equation Time-Steppers},
  author={Yuying Liu and J. Kutz and S. Brunton},
  journal={ArXiv},
  year={2020},
  volume={abs/2008.09768}
}
  • Yuying Liu, J. Kutz, S. Brunton
  • Published 2020
  • Computer Science, Mathematics, Physics
  • ArXiv
  • Nonlinear differential equations rarely admit closed-form solutions, thus requiring numerical time-stepping algorithms to approximate solutions. Further, many systems characterized by multiscale physics exhibit dynamics over a vast range of timescales, making numerical integration computationally expensive due to numerical stiffness. In this work, we develop a hierarchy of deep neural network time-steppers to approximate the flow map of the dynamical system over a disparate range of time-scales… CONTINUE READING
    3 Citations

    References

    SHOWING 1-10 OF 82 REFERENCES
    Learning data-driven discretizations for partial differential equations
    • 85
    • PDF
    Data Driven Governing Equations Approximation Using Deep Neural Networks
    • 69
    • Highly Influential
    • PDF
    Latent Space Physics: Towards Learning the Temporal Evolution of Fluid Flow
    • 98
    • PDF
    Multistep Neural Networks for Data-driven Discovery of Nonlinear Dynamical Systems
    • 107
    • PDF
    Long-time predictive modeling of nonlinear dynamical systems using neural networks
    • 38
    • PDF
    Neural Ordinary Differential Equations
    • 882
    • PDF