Filtering of wave equation in high dimension
Seminar Room 1, Newton Institute
The aim of this talk is to study a so-called data-model mismatch problem. It consists of two more or less independent parts. In the first part, we present infinite dimensional Kalman Filter for the advection equation on the torus. We see the velocity difference between the true signal and the model leads to various limit behaviors of the posterior mean. In the second part, Fourier diagonal Filter would be examined in the context of the Majda-McLaughlin-Tabak wave turbulence model. It is demonstrated that nonlinear wave interactions renormalize the dynamics, leading to a possible destruction of scaling structures in the bare wave systems. The Filter performance is improved when this renormalized dispersion relation is considered.