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. 2019 Dec 23;9:19728. doi: 10.1038/s41598-019-56212-5

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© The Author(s) 2019

Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.

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(a) First five principal components of the electric fields in the grating splitter dataset. (b) Performance of data-driven GMRES on the evaluation dataset when supplied with different number of principal components (~200 samples from the training set were used for computing the principal components) — the dotted line shows the mean residual, and the solid colored background indicates the region within one standard deviation around the mean residual. (c) Histogram of the residual after 100 data-driven GMRES iterations for different N computed over 100 randomly chosen samples from the evaluation dataset. The black vertical dashed line indicates the mean residual after 100 iterations of GMRES over the evaluation dataset.