Data-driven model reduction for stochastic Burgers equations

Understand

We present a class of efficient parametric closure models for 1D stochastic Burgers equations.

• Casting it as statistical learning of the flow map, we derive the parametric form by representing the unresolved high wavenumber Fourier modes as functionals of the resolved variables' trajectory.
• The reduced models are nonlinear autoregression (NAR) time series models, with coefficients estimated from data by least squares.
• The NAR models can accurately reproduce the energy spectrum, the invariant densities, and the autocorrelations.