Optimal Prediction for Hamiltonian Partial Differential Equations
Copyright policy )Optimal Prediction for Hamiltonian Partial Differential Equations
Optimal prediction methods compensate for a lack of resolution in the numerical solution of time-dependent differential equations through the use of prior statistical information. We present a new derivation of the basic methodology, show that field-theoretical perturbation theory provides a useful device for dealing with quasi-linear problems, and provide a nonlinear example that illuminates the difference between a pseudo-spectral method and an optimal prediction method with Fourier kernels. Along the way, we explain the differences and similarities between optimal prediction, the representer method in data assimilation, and duality methods for finding weak solutions. We also discuss the conditions under which a simple implementation of the optimal prediction method can be expected to perform well.
38 pages, 16 figures
- University of California, San Francisco United States
- Hebrew University of Jerusalem Israel
- University of California System United States
- Lawrence Berkeley National Laboratory United States
- The Hebrew University Israel
Numerical solutions to stochastic differential and integral equations, optimal prediction, Numerical Analysis, invariant measure, quasi-linear problems, Numerical Analysis (math.NA), pseudo-spectral method, Inference from stochastic processes and prediction, Hamiltonian partial differential equations, Stochastic partial differential equations (aspects of stochastic analysis), FOS: Mathematics, stochastic processes, PDEs with randomness, stochastic partial differential equations, Prediction theory (aspects of stochastic processes), inference from stochastic processes, perturbation theory
Numerical solutions to stochastic differential and integral equations, optimal prediction, Numerical Analysis, invariant measure, quasi-linear problems, Numerical Analysis (math.NA), pseudo-spectral method, Inference from stochastic processes and prediction, Hamiltonian partial differential equations, Stochastic partial differential equations (aspects of stochastic analysis), FOS: Mathematics, stochastic processes, PDEs with randomness, stochastic partial differential equations, Prediction theory (aspects of stochastic processes), inference from stochastic processes, perturbation theory
selected citations These citations are derived from selected sources.This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).23 popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.Average influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).Top 10% impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.Average
Citations provided by BIP!Popularity provided by BIP!