Variational Monte Carlo - Bridging concepts of machine learning and high dimensional partial differential equations
dc.bibliographicCitation.seriesTitle | WIAS Preprints | eng |
dc.bibliographicCitation.volume | 2544 | |
dc.contributor.author | Eigel, Martin | |
dc.contributor.author | Trunschke, Philipp | |
dc.contributor.author | Schneider, Reinhold | |
dc.contributor.author | Wolf, Sebastian | |
dc.date.accessioned | 2018-12-13T04:12:26Z | |
dc.date.available | 2019-06-28T08:03:09Z | |
dc.date.issued | 2018 | |
dc.description.abstract | A statistical learning approach for parametric PDEs related to Uncertainty Quantification is derived. The method is based on the minimization of an empirical risk on a selected model class and it is shown to be applicable to a broad range of problems. A general unified convergence analysis is derived, which takes into account the approximation and the statistical errors. By this, a combination of theoretical results from numerical analysis and statistics is obtained. Numerical experiments illustrate the performance of the method with the model class of hierarchical tensors. | eng |
dc.description.version | publishedVersion | eng |
dc.format | application/pdf | |
dc.identifier.issn | 2198-5855 | |
dc.identifier.uri | https://doi.org/10.34657/3468 | |
dc.identifier.uri | https://oa.tib.eu/renate/handle/123456789/1987 | |
dc.language.iso | eng | eng |
dc.publisher | Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik | eng |
dc.relation.doi | https://doi.org/10.20347/WIAS.PREPRINT.2544 | |
dc.relation.issn | 0946-8633 | eng |
dc.rights.license | This document may be downloaded, read, stored and printed for your own use within the limits of § 53 UrhG but it may not be distributed via the internet or passed on to external parties. | eng |
dc.rights.license | Dieses Dokument darf im Rahmen von § 53 UrhG zum eigenen Gebrauch kostenfrei heruntergeladen, gelesen, gespeichert und ausgedruckt, aber nicht im Internet bereitgestellt oder an Außenstehende weitergegeben werden. | ger |
dc.subject.ddc | 510 | eng |
dc.subject.other | Partial differential equations with random coefficients | eng |
dc.subject.other | tensor representation | eng |
dc.subject.other | tensor train | eng |
dc.subject.other | uncertainty quantification | eng |
dc.subject.other | stochastic finite element methods | eng |
dc.subject.other | log-normal | eng |
dc.subject.other | adaptive methods | eng |
dc.subject.other | ALS | eng |
dc.subject.other | low-rank | eng |
dc.subject.other | reduced basis methods | eng |
dc.title | Variational Monte Carlo - Bridging concepts of machine learning and high dimensional partial differential equations | eng |
dc.type | Report | eng |
dc.type | Text | eng |
tib.accessRights | openAccess | eng |
wgl.contributor | WIAS | eng |
wgl.subject | Mathematik | eng |
wgl.type | Report / Forschungsbericht / Arbeitspapier | eng |
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