Publikationen des Lehrstuhls Datenassimilation

Can one hear the depth of the water?

Autoren: M.A. Freitag, P.Kriz, T. Mach, J. M. Nicolaus (2023)

We discuss discrete-time dynamical systems depending on a parameter μ. Assuming that the system matrix A(μ) is given, but the parameter μ is unknown, we infer the most-likely parameter μm≈μ from an observed trajectory x of the dynamical system. We use parametric eigenpairs (vi(μ),lambdai(μ) of the system matrix A(μ) computed with Newton's method based on a Chebyshev expansion. We then represent x in the eigenvector basis defined by the vi(μ) and compare the decay of the components with predictions based on the lambdai(μ). The resulting estimates for μ are combined using a kernel density estimator to find the most likely value for μm and a corresponding uncertainty quantification.

Proceedings in Applied Mathematics and Mechanics

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