Approximation error approach in spatiotemporally chaotic models with application to Kuramoto–Sivashinsky equation
| Autor: | Janne M. J. Huttunen, Jari P. Kaipio, Heikki Haario |
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| Rok vydání: | 2018 |
| Předmět: |
Statistics and Probability
Partial differential equation 010504 meteorology & atmospheric sciences State-space representation Computer science Noise (signal processing) Applied Mathematics Bayesian probability Chaotic 01 natural sciences 010101 applied mathematics Reduction (complexity) Parameter identification problem Computational Mathematics Computational Theory and Mathematics Approximation error Applied mathematics 0101 mathematics 0105 earth and related environmental sciences |
| Zdroj: | Computational Statistics & Data Analysis. 123:13-31 |
| ISSN: | 0167-9473 |
| DOI: | 10.1016/j.csda.2018.01.015 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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