Reduced basis methods for Bayesian inverse problems 88
Accurate solution of Bayesian inverse uncertainty quantification problems combining reduced basis methods and reduction error models
... On the other hand, we develop suitable reduction error models (REMs) to quantify in an inexpensive way the error between the full-order and the reduced-order approximation of the forward[r] ...
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Accurate Solution of Bayesian Inverse Uncertainty Quantification Problems Combining Reduced Basis Methods and Reduction Error Models
... that nevertheless cannot be fully ascertained) and its quantification is essential in order to obtain precise and robust solutions to the inverse UQ problem. ROM uncertainty is indeed quite similar to the ...
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Basis mapping methods for forward and inverse problems
... of basis matrices B uu , B uv and B uv against inverse of thread count, using a multithreaded ...finite-dimensional basis representation x U ...between basis expansions may arise in numerical ...
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Variational Bayesian Approximation methods for inverse problems
... the Bayesian computations with this model, we use the property of Student-t which is modelling it via an infinite mixture of Gaussians, introducing thus hidden variables which are the ...the inverse ...
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Sequential Monte Carlo methods for Bayesian elliptic inverse problems
... these problems has been the development of algorithms with mesh-free mixing times, such as those highlighted in [8, 16]; these non-standard MCMC algorithms avoid the unnecessary penalties incurred by naive ...
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Probabilistic numerical methods for PDE-constrained Bayesian inverse problems
... inverse problems. This allows robust infer- ences to be made in inverse problems, even when the numerical scheme used to solve the forward problem is inaccurate, which is useful in cases where ...
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The Bayesian approach to inverse problems
... the Bayesian approach to inverse problems in differential ...the Bayesian approach to inverse ...Carlo methods, and measure-preserving reversible stochastic differential ...
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Certified reduced basis methods for parametrized saddle point problems
... The Reduced Basis Method 3 We emphasize that, even though coming from various fields with different objectives, the above model order reduction techniques share a common basic principle: They all can be ...
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Approximation of Bayesian inverse problems for PDEs
... such problems, regularization of some form is needed to counteract the resulting ...a Bayesian formulation of the problem, which leads to a notion of well posedness for inverse problems, at ...
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Adding Constraints to Bayesian Inverse Problems
... numerical methods have enabled models to be increasingly sophisticated and ...an inverse problem by us- ing observational data to specify model parameters so that the model output matches the observational ...
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Comparison between reduced basis and stochastic collocation methods for elliptic problems
... Reduced basis method, on the other hand, is a model reduction technique originally developed to solve parametric problems arising from the field of structure mechanics, fluid dynamics, ...stochastic ...
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Wavelet Methods and Inverse Problems
... a Bayesian framework, using a Markov chain Monte Carlo (MCMC) algo- ...of inverse problems, whereas in this thesis, inverse problems are divided into two ...
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Sparse deterministic approximation of Bayesian inverse problems
... (MC) methods, as measured by computational cost per unit error in predicted ...an inverse problem. One approach to such inverse problems is via the techniques of optimal control [2]; however ...
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Sparse determinisitc approximation of Bayesian inverse problems
... (MC) methods, as measured by computational cost per unit error in predicted ...an inverse problem. One approach to such inverse problems is via the techniques of optimal control [2]; however ...
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A Bayesian framework for inverse problems for quantitative biology
... quantitative methods in biology 1.6.1 Optimisation methods and inverse problems Optimisation methods and inverse problem frameworks are a natural candidate to provide ...
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Bayesian Asymptotics: Inverse Problems and Irregular Models
... these methods are not adaptive, in the sense that they rely on knowledge of the regularity ...the Bayesian approach with fixed Gaussian priors that is not adaptive has been recently studied in ...several ...
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Radiation Source Mapping with Bayesian Inverse Methods.
... with Bayesian Inverse ...Most methods to analyze these problems make restrictive assumptions about the distribution of the ...probabilistic Bayesian approach is used to solve the ...
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Continuous Methods for Elliptic Inverse Problems
... Clearly, the process finds the slope (tangent line) at the initial condition a(t 0 ) = a 0 , then at each iteration re-evaluates the slope at the new point. Connecting all of these line segments gives an approximation of ...
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Continuous Methods for Elliptic Inverse Problems
... Clearly, the process finds the slope (tangent line) at the initial condition a(t 0 ) = a 0 , then at each iteration re-evaluates the slope at the new point. Connecting all of these line segments gives an approximation of ...
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Ensemble Kalman methods for inverse problems
... Section 2 that the space A = span{ψ (j) } J j=1 will be chosen based on either draws from the prior µ 0 , with subscript R, or on the Karhunen-Lo´eve basis, with subscript KL. The forward model (43)-(45) is ...
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