Enabling Equation-Free Modeling via Diffusion Maps

  title={Enabling Equation-Free Modeling via Diffusion Maps},
  author={Tracy Chin and Jacob Ruth and Clayton Sanford and Rebecca Santorella and Paul Carter and Bj{\"o}rn Sandstede},
  journal={Journal of Dynamics and Differential Equations},
Equation-free modeling aims at extracting low-dimensional macroscopic dynamics from complex highdimensional systems that govern the evolution of microscopic states. This algorithm relies on lifting and restriction operators that map macroscopic states to microscopic states and vice versa. Combined with simulations of the microscopic state, this algorithm can be used to apply Newton solvers to the implicitly defined low-dimensional macroscopic system or solve it more efficiently using direct… 
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  • R. Coifman, S. Lafon, S. Zucker
  • Mathematics
    Proceedings of the National Academy of Sciences of the United States of America
  • 2005
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