5 papers
Estimating the uncertainty in underresolved nonlinear dynamics
Alexandre J. Chorin, Ole H. Hald
The Mori-Zwanzig formalism of statistical mechanics is used to estimate the uncertainty caused by underresolution in the solution of a nonlinear dynamical system. A general approac…
Application of the t-model of optimal prediction to the estimation of the rate of decay of solutions of the Euler equations in two and three dimensions
Ole H. Hald, Panagiotis Stinis
The "t-model" for dimensional reduction is applied to the estimation of the rate of decay of solutions of the Burgers equation and of the Euler equations in two and three space dim…
Non-Markovian Optimal Prediction
Alexandre J. Chorin, Ole H. Hald, Raz Kupferman
Optimal prediction methods compensate for a lack of resolution in the numerical solution of complex problems through the use of prior statistical information. We know from previous…
Optimal prediction and the Klein-Gordon equation
O. H. Hald
The method of optimal prediction is applied to calculate the future means of solutions to the Klein-Gordon equation. It is shown that in an appropriate probability space, the diffe…
A Formula for Finding a Potential from Nodal Lines
Joyce R. McLaughlin, Ole H. Hald
In this announcement we consider an eigenvalue problem which arises in the study of rectangular membranes. The mathematical model is an elliptic equation, in potential form, with D…