| Abstract: |
| Many dynamical systems of interest in science and engineering are too complex or computationally expensive to fully resolve, even though only a relatively small subset of the degrees of freedom are observable or of direct interest. In these situations, it is useful to have low-dimensional models that can predict the evolution of the variables of interest without reference to the remaining degrees of freedom, and reproduce their statistics at an acceptable cost. This talk concerns a discrete-time, parametric approach to the problem of constructing reduced models from data. I will discuss some of the theoretical and practical issues that arise, including the representation of memory and noise effects. The approach is illustrated using the Kuramoto-Sivashinsky PDE, a prototypical model of spatiotemporal chaos. Time-permitting, I will also discuss connections between this method and the Mori-Zwanzig formalism of nonequilibrium statistical mechanics. This is joint work with Alexandre Chorin and Fei Lu. |
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