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Optimal Prediction and Dimensional Reduction

Optimal prediction is an adaptation of a formalism from irreversible statistical mechanics to the reduction of the dimension of large systems of time-dependent differential equations, and to the optimal estimation of solutions of differential equations when the data are noise or incomplete. It reduces such problems to the solution of generalized Langevin equations, where the memory and noise terms are found numerically. It is used in climate modeling and in problems of condensed matter physics.