Goal-oriented Uncertainty Quantification for Inverse Problems via Variational Encoder-Decoder Networks
| Title: | Goal-oriented Uncertainty Quantification for Inverse Problems via Variational Encoder-Decoder Networks |
|---|---|
| Authors: | Afkham, Babak Maboudi, Chung, Julianne, Chung, Matthias |
| Publication Year: | 2023 |
| Collection: | Computer Science Mathematics |
| Subject Terms: | Mathematics - Numerical Analysis, Computer Science - Machine Learning, 15A29, 6208, 68U07 |
| More Details: | In this work, we describe a new approach that uses variational encoder-decoder (VED) networks for efficient goal-oriented uncertainty quantification for inverse problems. Contrary to standard inverse problems, these approaches are \emph{goal-oriented} in that the goal is to estimate some quantities of interest (QoI) that are functions of the solution of an inverse problem, rather than the solution itself. Moreover, we are interested in computing uncertainty metrics associated with the QoI, thus utilizing a Bayesian approach for inverse problems that incorporates the prediction operator and techniques for exploring the posterior. This may be particularly challenging, especially for nonlinear, possibly unknown, operators and nonstandard prior assumptions. We harness recent advances in machine learning, i.e., VED networks, to describe a data-driven approach to large-scale inverse problems. This enables a real-time goal-oriented uncertainty quantification for the QoI. One of the advantages of our approach is that we avoid the need to solve challenging inversion problems by training a network to approximate the mapping from observations to QoI. Another main benefit is that we enable uncertainty quantification for the QoI by leveraging probability distributions in the latent space. This allows us to efficiently generate QoI samples and circumvent complicated or even unknown forward models and prediction operators. Numerical results from medical tomography reconstruction and nonlinear hydraulic tomography demonstrate the potential and broad applicability of the approach. Comment: 28 pages, 13 figures |
| Document Type: | Working Paper |
| Access URL: | http://arxiv.org/abs/2304.08324 |
| Accession Number: | edsarx.2304.08324 |
| Database: | arXiv |
| FullText | Text: Availability: 0 CustomLinks: – Url: http://arxiv.org/abs/2304.08324 Name: EDS - Arxiv Category: fullText Text: View this record from Arxiv MouseOverText: View this record from Arxiv – Url: https://resolver.ebsco.com/c/xy5jbn/result?sid=EBSCO:edsarx&genre=article&issn=&ISBN=&volume=&issue=&date=20230417&spage=&pages=&title=Goal-oriented Uncertainty Quantification for Inverse Problems via Variational Encoder-Decoder Networks&atitle=Goal-oriented%20Uncertainty%20Quantification%20for%20Inverse%20Problems%20via%20Variational%20Encoder-Decoder%20Networks&aulast=Afkham%2C%20Babak%20Maboudi&id=DOI: Name: Full Text Finder (for New FTF UI) (s8985755) Category: fullText Text: Find It @ SCU Libraries MouseOverText: Find It @ SCU Libraries |
|---|---|
| Header | DbId: edsarx DbLabel: arXiv An: edsarx.2304.08324 RelevancyScore: 1051 AccessLevel: 3 PubType: Report PubTypeId: report PreciseRelevancyScore: 1051.01843261719 |
| IllustrationInfo | |
| Items | – Name: Title Label: Title Group: Ti Data: Goal-oriented Uncertainty Quantification for Inverse Problems via Variational Encoder-Decoder Networks – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Afkham%2C+Babak+Maboudi%22">Afkham, Babak Maboudi</searchLink><br /><searchLink fieldCode="AR" term="%22Chung%2C+Julianne%22">Chung, Julianne</searchLink><br /><searchLink fieldCode="AR" term="%22Chung%2C+Matthias%22">Chung, Matthias</searchLink> – Name: DatePubCY Label: Publication Year Group: Date Data: 2023 – Name: Subset Label: Collection Group: HoldingsInfo Data: Computer Science<br />Mathematics – Name: Subject Label: Subject Terms Group: Su Data: <searchLink fieldCode="DE" term="%22Mathematics+-+Numerical+Analysis%22">Mathematics - Numerical Analysis</searchLink><br /><searchLink fieldCode="DE" term="%22Computer+Science+-+Machine+Learning%22">Computer Science - Machine Learning</searchLink><br /><searchLink fieldCode="DE" term="%2215A29%2C+6208%2C+68U07%22">15A29, 6208, 68U07</searchLink> – Name: Abstract Label: Description Group: Ab Data: In this work, we describe a new approach that uses variational encoder-decoder (VED) networks for efficient goal-oriented uncertainty quantification for inverse problems. Contrary to standard inverse problems, these approaches are \emph{goal-oriented} in that the goal is to estimate some quantities of interest (QoI) that are functions of the solution of an inverse problem, rather than the solution itself. Moreover, we are interested in computing uncertainty metrics associated with the QoI, thus utilizing a Bayesian approach for inverse problems that incorporates the prediction operator and techniques for exploring the posterior. This may be particularly challenging, especially for nonlinear, possibly unknown, operators and nonstandard prior assumptions. We harness recent advances in machine learning, i.e., VED networks, to describe a data-driven approach to large-scale inverse problems. This enables a real-time goal-oriented uncertainty quantification for the QoI. One of the advantages of our approach is that we avoid the need to solve challenging inversion problems by training a network to approximate the mapping from observations to QoI. Another main benefit is that we enable uncertainty quantification for the QoI by leveraging probability distributions in the latent space. This allows us to efficiently generate QoI samples and circumvent complicated or even unknown forward models and prediction operators. Numerical results from medical tomography reconstruction and nonlinear hydraulic tomography demonstrate the potential and broad applicability of the approach.<br />Comment: 28 pages, 13 figures – Name: TypeDocument Label: Document Type Group: TypDoc Data: Working Paper – Name: URL Label: Access URL Group: URL Data: <link linkTarget="URL" linkTerm="http://arxiv.org/abs/2304.08324" linkWindow="_blank">http://arxiv.org/abs/2304.08324</link> – Name: AN Label: Accession Number Group: ID Data: edsarx.2304.08324 |
| PLink | https://login.libproxy.scu.edu/login?url=https://search.ebscohost.com/login.aspx?direct=true&site=eds-live&scope=site&db=edsarx&AN=edsarx.2304.08324 |
| RecordInfo | BibRecord: BibEntity: Subjects: – SubjectFull: Mathematics - Numerical Analysis Type: general – SubjectFull: Computer Science - Machine Learning Type: general – SubjectFull: 15A29, 6208, 68U07 Type: general Titles: – TitleFull: Goal-oriented Uncertainty Quantification for Inverse Problems via Variational Encoder-Decoder Networks Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Afkham, Babak Maboudi – PersonEntity: Name: NameFull: Chung, Julianne – PersonEntity: Name: NameFull: Chung, Matthias IsPartOfRelationships: – BibEntity: Dates: – D: 17 M: 04 Type: published Y: 2023 |
| ResultId | 1 |