A modified Levenberg-Marquardt algorithm for quasi-linear geostatistical inversing

By Wolfgang Nowak, Olaf A. Cirpka. 2004

88 citations recorded by the source corpus.

Subfields: Environmental Engineering, Geophysics

View Paper: https://www.semanticscholar.org/paper/bcf996881fe2b2429f0af6b2d6f83dd3c7f927ec

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Citations in the corpus

Two‐dimensional characterization of hydraulic heterogeneity by multiple pumping tests (2007, methodology): “We stabilize the approach by a modified Levenberg-Marquardt method [Nowak and Cirpka, 2004], compute the sensitivities by the continuous adjoint-state method [Sun and Yeh, 1990], and accelerate the matrixmatrix multiplications involved by periodic embedding and spectral methods [Nowak et al., 2003].”
Geostatistical inference of hydraulic conductivity and dispersivities from hydraulic heads and tracer data (2006, methodology): “[40] In practice, we stabilize the iteration procedure in equations (12)–(16) by a modified Levenberg-Marquardt algorithm [Nowak and Cirpka, 2004] and evaluate ~ HkQss~ Hk , ~ Hk Gss~ Hk , Qss~ Hk T and Gss ~ Hk T using FFT-based methods [Nowak et al.”
Efficient geostatistical inverse methods for structured and unstructured grids (2006, methodology): “To stabilize the method, we apply the Levenberg-Marquardt method [Levenberg , 1944; Marquardt, 1963; Nowak and Cirpka, 2004], which suppresses oscillations by amplifying the diagonal entries of the left-hand side matrix in equation (38).”
A hypothesis‐driven approach to optimize field campaigns (2012, methodology): “For mildly nonlinear cases, we recommend the quasilinear geostatistical approach [Kitanidis, 1995] and its upgrades [e.g., Nowak and Cirpka, 2004], ensemble Kalman filters [Zhang et al., 2005; Nowak, 2009], and biasaware modifications of it [e.g., Drécourt et al., 2006; Kollat et al., 2011], or…”
A conceptual comparison of the Cuckoo-search, particle swarm optimization, differential evolution and artificial bee colony algorithms (2011, methodology): “…functions the solution of which is either impossible or extremely difficult by using the classical optimization techniques (Karaboga and Akay 2009a; Nowak and Cirpka 2004; Clerc and Kennedy 2002; Trelea 2003; Dorigo et al. 1996; Ong et al. 2006; Storn and Price 1997; Yang and Deb 2010; Das et al.…”
Bayesian geostatistical design: Task‐driven optimal site investigation when the geostatistical model is uncertain (2010, background): “This approach has already proven useful to generalize geostatistical inversion [Nowak and Cirpka, 2004; Fritz et al., 2009].”
Best unbiased ensemble linearization and the quasi‐linear Kalman ensemble generator (2009, methodology): “For the indirect data, it has a quasi-linear iteration scheme, stabilized by a geostatistically driven Levenberg-Marquardt technique [Nowak and Cirpka, 2004].”
Large‐scale hydraulic tomography and joint inversion of head and tracer data using the Principal Component Geostatistical Approach (PCGA) (2014, methodology): “For strongly nonlinear problems, the Levenberg-Marquardt method [Nowak and Cirpka, 2004] or a line search [Zanini and Kitanidis, 2009; Liu and Kitanidis, 2011] can be adopted for the better convergence.”