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. 2020 May 12;14:36. doi: 10.3389/fncom.2020.00036

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Copyright © 2020 Thiem, Kooshkbaghi, Bertalan, Laing and Kevrekidis.

This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

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The training and validation loss of the neural network training for: (A) the Δt = 0.01 time horizon, and (B) the Δt = 0.05 time horizon. (C) Plots of the learned, neural network right-hand-side for two different time horizons (blue, purple) and the analytically derived right-hand-side (orange). A forward Euler approximation (black) and its geometric harmonic interpolation (green) are included for comparison. (D) The error behaves similarly for both time horizons, with a magnitude < 0.01 for the entirety of the domain.