Multilevel Adaptive Sparse Leja Approximations for Bayesian Inverse Problems
نویسندگان
چکیده
منابع مشابه
Multilevel Sparse Approximate Inverse Preconditioners for Adaptive Mesh Refinement∗
We present an efficient and effective preconditioning method for time-dependent simulations with dynamic, adaptive mesh refinement and implicit time integration. Adaptive mesh refinement greatly improves the efficiency of simulations where the solution develops steep gradients in small regions of the computational domain that change over time. Unfortunately, adaptive mesh refinement also introd...
متن کاملAn efficient Bayesian inference approach to inverse problems based on adaptive sparse grid collocation method
A new approach for modeling inverse problems using a Bayesian inference method is introduced. The Bayesian approach considers the unknown parameters as random variables and seeks the probabilistic distribution of the unknowns. By introducing the concept of the stochastic prior state space to the Bayesian formulation, we reformulate the deterministic forward problem as a stochastic one. The adap...
متن کاملAn efficient Bayesian inference approach to inverse problems based on an adaptive sparse grid collocation method
A new approach to modeling inverse problems using a Bayesian inference method is introduced. The Bayesian approach considers the unknown parameters as random variables and seeks the probabilistic distribution of the unknowns. By introducing the concept of the stochastic prior state space to the Bayesian formulation, we reformulate the deterministic forward problem as a stochastic one. The adapt...
متن کاملMultilevel Methods for Inverse Bioelelectric Field Problems
The reconstruction of bioelectric fields from non-invasive measurements can be used as a powerful new diagnostic tool in cardiology and neurology. Mathematically, the reconstruction of a bioelectric field can be modeled as an inverse problem for a potential equation. This problem is ill-posed and requires special treatment, in particular either regularization or an otherwise suitable restrictio...
متن کاملAdaptive Bayesian Networks for Multilevel Student Modelling
In this paper we present an integrated theoretical approach for student modelling based on an Adaptive Bayesian Network. A mathematical formalization of the Adaptive Bayesian Network is provided, and new question selection criteria presented. Using this theoretical framework, a tool to assist in the diagnosis process has been implemented. This tool allows the definition of Bayesian Adaptive Tes...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: SIAM Journal on Scientific Computing
سال: 2020
ISSN: 1064-8275,1095-7197
DOI: 10.1137/19m1260293