Approximation errors in nonstationary inverse problems
By Janne M. J. Huttunen, Jari P. Kaipio. 2007
64 citations recorded by the source corpus.
Inverse problems are known to be very intolerant to both data errors and errors in the forward model. With several inverse problems the adequately accurate forward model can turn out to be computationally excessively complex. The Bayesian framework for inverse problems has recently been shown to enable the adoption of highly approximate forward models. This approach is based on the modelling of the associated approximation errors that are incorporated in the construction of the computational model. In this paper we investigate the extension of the approximation error theory to nonstationary inverse problems. We develop the basic framework for linear nonstationary inverse problems that allows one to use both highly reduced states and extended time steps. As an example we study the one dimensional heat equation.
Subfields: Applied Mathematics, Artificial Intelligence, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/91fa24aab28f3683bbcf1fc1f59993950cc723e8
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In Applied Mathematics
In Artificial Intelligence
- Karen E. Willcox
- Max D. Gunzburger
- Benjamin Peherstorfer
- Andrew M. Stuart
- Mark A. Girolami
- G. Em Karniadakis
- Masoumeh Dashti
- Sari Lasanen
In Mathematical Physics
Citations in the corpus
- Survey of multifidelity methods in uncertainty propagation, inference, and optimization (2018, background): “Extensions to time-dependent problems are presented in [106, 105].”
- Inverse problems: A Bayesian perspective (2010, methodology): “The idea concluding the proof of the first part of Theorem 5.4 is standard in the theory of calculus of variations: see Dacarogna (1989, Chapter 3, Theorem 1.1).”