Parameter estimation and inverse problems

By R. Aster, Brian Borchers, C. Thurber. 2005

2,524 citations recorded by the source corpus.

Subfields: Control and Systems Engineering, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/090675c5a071208fcdfb57528217d8ca25428b3f

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In Control and Systems Engineering

In Mathematical Physics

Citations in the corpus

Regularization in model updating (2008, methodology): “[9] discussed a number of well-established methods and approaches within the field and Tarantola [10] described statistical approaches to inverse problems with a strong emphasis on the application of Monte Carlo methods.”
Integrated environmental modeling: A vision and roadmap for the future (2013, background): “Several textbooks on these subjects have been produced in recent years (Menke, 2012; Aster et al., 2005 from geophysics; Beven, 2009; Clark et al., 2011; Hill and Tiedeman, 2007 from hydrology; Saltelli et al., 2008 from econometrics), and an active scienti ﬁ c community continues to explore new…”
Stochastic spectral methods for efficient Bayesian solution of inverse problems (2005, background): “Bayesian approaches to inverse problems have seen much recent interest [3,5,2], with applications ranging from geophysics [6,7] and climate modeling [8] to heat transfer [9,10].”
Numerical Simulation of the 2011 Tohoku Tsunami Based on a New Transient FEM Co-seismic Source: Comparison to Far- and Near-Field Observations (2013, background): “The knee of the L-curve is the preferred solution, which is a compromise between fitting the data versus satisfying the smoothing constraints (ASTER et al. 2005) Vol.”
Tropospheric emission spectrometer: retrieval method and error analysis (2006, methodology): “The following criteria are used in conjunction to test for convergence [25], [26] : (27) (28) (29”
Solving Irregular and Data-enriched Differential Equations using Deep Neural Networks (2019, neutral): “Many of the more traditional approaches, including data-informed parameter estimation methods [23] and real-time filtering [24], are frequently incorporated into more standard forward PDE solvers.”
A new method for parameter estimation in probabilistic models: Minimum probability flow (2020, background): “This is a challenging problem in many interesting cases [7, 9, 10].”
Transdimensional tomography with unknown data noise (2012, methodology): “The linear trend described earlier is a common observation in real data sets and is called a proportional effect (Aster et al. 2005).”
Seismic inversion based on L1-norm misfit function and total variation regularization (2014, neutral): “The other techniques for L1-norm minimization methods are based on the interior-point and iteratively re-weighted least square (Aster et al., 2005, 2013; Coleman and Li, 1992; Portnoy and Koenker, 1997; Scales et al., 1988; Watson, 2000). The iteratively re-weighted least square (IRLS) method is the”
Imaging of groundwater with nuclear magnetic resonance (2008, methodology): “(23) is a common Fredholm integral equation of the first kind, a form that is quite common in geophysical inverse methods [24].”
Calibration‐constrained Monte Carlo analysis of highly parameterized models using subspace techniques (2009, methodology): “…is calculated from observations using matrix G, such that: p ¼ Gy ð6Þ A variety of methods have been developed to obtain a suitable G. Tonkin and Doherty [2005] contrast methods based on Tikhonov regularization [Tikhonov and Arsenin, 1977] with those that employ TSVD [e.g., Aster et al., 2005].”
Dimensionality reduction and polynomial chaos acceleration of Bayesian inference in inverse problems (2008, background): “Bayesian approaches to inverse problems have received much recent interest [4, 48, 49], with applications ranging from geophysics [50, 51] and climate modeling [52] to heat transfer [20, 53].”