Inverse problem theory - and methods for model parameter estimation

By Albert Tarantola. 2004

6,279 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Mathematical Physics, Statistics and Probability, Numerical Methods & Scientific Computing

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

In Computational Theory and Mathematics

In Mathematical Physics

In Statistics and Probability

In Numerical Methods & Scientific Computing

Citations in the corpus

Meta-learning with differentiable closed-form solvers (2018, background): “The regularization term can be seen as a prior gaussian distribution of the parameters in a Bayesian interpretation, or more simply Tikhonov regularization (Tarantola, 2005).”
Can we constrain the interior structure of rocky exoplanets from mass and radius measurements (2015, methodology): “…information content of data, i.e. the degree to which data constrain internal structure, we compute the Shannon entropy measure (Hposterior/Hprior) (Tarantola 2005), which allows comparison of prior and posterior pdfs. Article number, page 7 of 19 If Hposterior/Hprior → 1, data are only weakly…”
Finite‐frequency tomography using adjoint methods—Methodology and examples using membrane surface waves (2007, methodology): “Let us suppose we have a particular model m, and we wish to obtain an updated model m + δm that brings us closer to a minimum of the misfit function χ (Nolet 1987; Tarantola 2005, appendix 6.22).”
Atmospheric muons as an imaging tool (2019, background): “It is outside the scope of this review to provide a treatise on this topic, suffices to say that the regularisation algorithms that have been developed can mitigate many of the issues and are based either on minimum squares formulations [116, 117] or Bayesian ones [118].”
Simulator-free solution of high-dimensional stochastic elliptic partial differential equations using deep neural networks (2019, neutral): “This inverse problem is solved in a Bayesian way [75, 76] as follows.”
Discretization-invariant Bayesian inversion and Besov space priors (2009, neutral): “For general reference on Bayesian inversion see [33, 48, 27, 63, 13].”
Seismic tomography of the southern California crust based on spectral‐element and adjoint methods (2010, background): “From a Bayesian perspective, the final model (m16) represents the mean model of a posterior distribution of possible models (CM) (Tarantola 2005).”
Joint inversion of seismic and gravity data for lunar composition and thermal state (2007, methodology): “As advocated by Mosegaard & Tarantola (1995) and Tarantola (2004), we can also display a collection of models from the posterior pdf .”
Neural operators for accelerating scientific simulations and design (2023, neutral): “Additionally, numerical methods are not generally differentiable, thus making inverse problems and design optimization expensive and slow [4].”
Data Assimilation for Numerical Weather Prediction: A Review (2009, methodology): “We will mention the recent book by Aster, Borchers and Thurber[7], Tarantola[352] and Sun[341] to quote but a few.”
Hessian kernels of seismic data functionals based upon adjoint techniques (2011, background): “(4) reveals that H(m̃) is the inverse posterior covariance matrix in the vicinity of m̃ (e.g. Tarantola 2005).”