Variational Monte Carlo—bridging concepts of machine learning and high-dimensional partial differential equations
A statistical learning approach for high-dimensional 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...
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Published in | Advances in computational mathematics Vol. 45; no. 5-6; pp. 2503 - 2532 |
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Main Authors | , , , |
Format | Journal Article |
Language | English |
Published |
New York
Springer US
01.12.2019
Springer Nature B.V |
Subjects | |
Online Access | Get full text |
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Summary: | A statistical learning approach for high-dimensional 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. |
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Bibliography: | ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14 |
ISSN: | 1019-7168 1572-9044 |
DOI: | 10.1007/s10444-019-09723-8 |