Approximation error approach in spatiotemporally chaotic models with application to Kuramoto-Sivashinsky equation

Model reduction, parameter uncertainties and state estimation in spatiotemporal problems induced by chaotic partial differential equations is considered. The model reduction and parameter uncertainties induce a specific structure for the state noise process, and also modify the observation noise model. The nonstationary Bayesian approximation error approach (BAE) is employed to construct the state evolution and observation models. Earlier results have shown that the effects of severe model reduction and parameter uncertainties can be handled with the nonstationary BAE. The applicability of BAE to chaotic state evolution problems has not been investigated previously. The Kuramoto-Sivashinsky equation is considered with noisy measurements and, in addition, the related state space model identification problem is also considered. The results suggest that the nonstationary BAE is a potentially feasible approach for reduced order chaotic models and, when feasible, the accuracy of the state estimates is comparable to that of respective non-reduced order model.