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• W4380886155 abstract "In this paper, we consider a Bayesian inverse problem modeled by elliptic partial differential equations (PDEs). Specifically, we propose a data-driven and model-based approach to accelerate the Hamiltonian Monte Carlo (HMC) method in solving large-scale Bayesian inverse problems. The key idea is to exploit (model-based) and construct (data-based) intrinsic approximate low-dimensional structure of the underlying problem which consists of two components—a training component that computes a set of data-driven basis to achieve significant dimension reduction in the solution space, and a fast solving component that computes the solution and its derivatives for a newly sampled elliptic PDE with the constructed data-driven basis. Hence we develop an effective data and model-based approach for the Bayesian inverse problem and overcome the typical computational bottleneck of HMC—repeated evaluation of the Hamiltonian involving the solution (and its derivatives) modeled by a complex system, a multiscale elliptic PDE in our case. Finally, we present numerical examples to demonstrate the accuracy and efficiency of the proposed method." @default.
• W4380886155 created "2023-06-17" @default.
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• W4380886155 date "2023-06-16" @default.
• W4380886155 modified "2023-10-13" @default.
• W4380886155 title "A data-driven and model-based accelerated Hamiltonian Monte Carlo method for Bayesian elliptic inverse problems" @default.
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• W4380886155 doi "https://doi.org/10.1007/s11222-023-10262-y" @default.
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