Statistical and deterministic inverse methods in the geosciences: introduction, review, and application to the nonlinear diffusion equation

DOI10.1007/s13137-021-00186-yzbMath1476.86001OpenAlexW3198939013MaRDI QIDQ2062363

Georg S. Reuber

Publication date: 27 December 2021

Published in: GEM - International Journal on Geomathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s13137-021-00186-y

zbMATH Keywords

sensitivity analysisnonlinear diffusion equationinverse methodsinterdisciplinary overview

Mathematics Subject Classification ID

Geostatistics (86A32) Computational methods for problems pertaining to geophysics (86-08) Potentials, prospecting (86A20) Research exposition (monographs, survey articles) pertaining to geophysics (86-02)

Cites Work

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• Nonlinear total variation based noise removal algorithms
• Using inexact gradients in a multilevel optimization algorithm
• Identification of uncertainties in the shape of geophysical objects with level sets and the adjoint method
• Optimization of mesh hierarchies in multilevel Monte Carlo samplers
• Automated solution of differential equations by the finite element method. The FEniCS book
• The random walk Metropolis: linking theory and practice through a case study
• Multilevel optimization: algorithms and applications
• Hierarchical Bayesian level set inversion
• Automated rejection sampling from product of distributions
• A PDE-based fast local level set method
• Adjoint-based inversion for porosity in shallow reservoirs using pseudo-transient solvers for non-linear hydro-mechanical processes
• Minimization of functions having Lipschitz continuous first partial derivatives
• A level set method for inverse problems
• Ensemble Kalman methods for inverse problems
• A Stochastic Newton MCMC Method for Large-Scale Statistical Inverse Problems with Application to Seismic Inversion
• Solving large-scale PDE-constrained Bayesian inverse problems with Riemann manifold Hamiltonian Monte Carlo
• Simulating Hamiltonian Dynamics
• A comparative study of structural similarity and regularization for joint inverse problems governed by PDEs
• Adaptive Rejection Sampling for Gibbs Sampling
• Equation of State Calculations by Fast Computing Machines
• Monte Carlo sampling methods using Markov chains and their applications
• Conditioning of Quasi-Newton Methods for Function Minimization
• A Simplex Method for Function Minimization
• An introduction to the adjoint approach to design

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