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. 2024 Feb 28;15:1834. doi: 10.1038/s41467-024-45323-x

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© The Author(s) 2024

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 licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence 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 licence, visit http://creativecommons.org/licenses/by/4.0/.

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Fig. 4 — a Computational domain and equations of the FOM. b Error metrics (NRMSE and Pearson dissimilarity) of LDNets for different number of latent variables (d_s = 1, 5 and 10). The training dataset consists of 80 simulations with T = 20, while the test dataset comprises 200 simulations with T = 40. The blue lines refer to the test error obtained in the interval t ∈ [0, 20] (that is the same interval seen during training), while orange lines refer to the test error in the interval t ∈ [0, 40]. c A snapshot of the velocity field within the interval t ∈ [0, 20] (interpolation interval) of a testing sample. d A snapshot of the velocity field within the interval t ∈ [20, 40] (extrapolation interval) of a testing sample. For an animated version of this figure, see Supplementary Movies 1–10.