Beating the curse of dimension with accurate statistics for the Fokker–Planck equation in complex turbulent systems
Abstract
Solving the Fokker–Planck equation for high-dimensional complex dynamical systems is an important issue. Effective strategies are developed and incorporated into efficient statistically accurate algorithms for solving the Fokker–Planck equations associated with a rich class of high-dimensional nonlinear turbulent dynamical systems with strong non-Gaussian features. These effective strategies exploit a judicious block decomposition of high-dimensional conditional covariance matrices and statistical symmetry to facilitate an extremely efficient parallel computation and a significant reduction of sample numbers. The resulting algorithms can efficiently solve the Fokker–Planck equation in much higher dimensions even with orders in the millions and thus beat the curse of dimension. Skillful behavior of the algorithms is illustrated for highly non-Gaussian systems in excitable media and geophysical turbulence.
Document Details
- Document Type
- Pub Defense Publication
- Publication Date
- Nov 20, 2017
- Source ID
- 10.1073/pnas.1717017114
Entities
People
- Andrew J. Majda
- Nan Chen
Organizations
- New York University
- Office of Naval Research