A Multi-level procedure for enhancing accuracy of machine learning algorithms
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Date
2019-09Type
- Report
ETH Bibliography
yes
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Abstract
We propose a multi-level method to increase the accuracy of machine learning algorithms for approximating observables in scientific computing, particularly those that arise in systems modeled by differential equations. The algorithm relies on judiciously combining a large number of computationally cheap training data on coarse resolutions with a few expensive training samples on fine grid resolutions. Theoretical arguments for lowering the generalization error, based on reducing the variance of the underlying maps, are provided and numerical evidence, indicating significant gains over underlying single-level machine learning algorithms, are presented. Moreover, we also apply the multi-level algorithm in the context of forward uncertainty quantification and observe a considerable speed-up over competing algorithms. Show more
Publication status
publishedExternal links
Journal / series
SAM Research ReportVolume
Publisher
Seminar for Applied Mathematics, ETH ZurichSubject
machine learning; Multi-level Monte Carlo; multi-level; deep learning; uncertainty quantificationsOrganisational unit
03851 - Mishra, Siddhartha / Mishra, Siddhartha
Funding
770880 - Computation and analysis of statistical solutions of fluid flow (EC)
Related publications and datasets
Is previous version of: http://hdl.handle.net/20.500.11850/450535
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ETH Bibliography
yes
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