title: Parametric reduced models for the nonlinear Schrödinger equation.
abstract: Reduced models for the (defocusing) nonlinear Schrödinger equation are developed. In particular, we develop reduced models that only involve the low-frequency modes given noisy observations of these modes. The ansatz of the reduced parametric models are obtained by employing a rational approximation and a colored-noise approximation, respectively, on the memory terms and the random noise of a generalized Langevin equation that is derived from the standard Mori-Zwanzig formalism. The parameters in the resulting reduced models are inferred from noisy observations with a recently developed ensemble Kalman filter-based parametrization method. The forecasting skill across different temperature regimes are verified by comparing the moments up to order four, a two-time correlation function statistics, and marginal densities of the coarse-grained variables.
authors.affiliation: Department of Mathematics, the Pennsylvania State University, University Park, Pennsylvania 16802-6400, USA.|Department of Meteorology, the Pennsylvania State University, University Park, Pennsylvania 16802-5013, USA.
authors.forename: John
authors.initials: J
authors.lastname: Harlim
authors.affiliation: Department of Mathematics, the Pennsylvania State University, University Park, Pennsylvania 16802-6400, USA.
authors.forename: Xiantao
authors.initials: X
authors.lastname: Li