File Download
There are no files associated with this item.
Links for fulltext
(May Require Subscription)
- Publisher Website: 10.1007/s11222-023-10262-y
- Scopus: eid_2-s2.0-85162021345
- WOS: WOS:001009223800001
- Find via
Supplementary
- Citations:
- Appears in Collections:
Article: A data-driven and model-based accelerated Hamiltonian Monte Carlo method for Bayesian elliptic inverse problems
Title | A data-driven and model-based accelerated Hamiltonian Monte Carlo method for Bayesian elliptic inverse problems |
---|---|
Authors | |
Keywords | Bayesian inversion Elliptic inverse problems Hamiltonian Monte Carlo (HMC) method Model reduction Proper orthogonal decomposition (POD) |
Issue Date | 16-Jun-2023 |
Publisher | Springer |
Citation | Statistics and Computing, 2023, v. 33, n. 4 How to Cite? |
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. |
Persistent Identifier | http://hdl.handle.net/10722/331140 |
ISSN | 2023 Impact Factor: 1.6 2023 SCImago Journal Rankings: 0.923 |
ISI Accession Number ID |
DC Field | Value | Language |
---|---|---|
dc.contributor.author | Li, Sijing | - |
dc.contributor.author | Zhang, Cheng | - |
dc.contributor.author | Zhang, Zhiwen | - |
dc.contributor.author | Zhao, Hongkai | - |
dc.date.accessioned | 2023-09-21T06:53:05Z | - |
dc.date.available | 2023-09-21T06:53:05Z | - |
dc.date.issued | 2023-06-16 | - |
dc.identifier.citation | Statistics and Computing, 2023, v. 33, n. 4 | - |
dc.identifier.issn | 0960-3174 | - |
dc.identifier.uri | http://hdl.handle.net/10722/331140 | - |
dc.description.abstract | <p>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.<br></p> | - |
dc.language | eng | - |
dc.publisher | Springer | - |
dc.relation.ispartof | Statistics and Computing | - |
dc.subject | Bayesian inversion | - |
dc.subject | Elliptic inverse problems | - |
dc.subject | Hamiltonian Monte Carlo (HMC) method | - |
dc.subject | Model reduction | - |
dc.subject | Proper orthogonal decomposition (POD) | - |
dc.title | A data-driven and model-based accelerated Hamiltonian Monte Carlo method for Bayesian elliptic inverse problems | - |
dc.type | Article | - |
dc.identifier.doi | 10.1007/s11222-023-10262-y | - |
dc.identifier.scopus | eid_2-s2.0-85162021345 | - |
dc.identifier.volume | 33 | - |
dc.identifier.issue | 4 | - |
dc.identifier.eissn | 1573-1375 | - |
dc.identifier.isi | WOS:001009223800001 | - |
dc.identifier.issnl | 0960-3174 | - |