==== Front Eur Phys J E Soft Matter Eur Phys J E Soft Matter The European Physical Journal. E, Soft Matter 1292-8941 1292-895X Springer Berlin Heidelberg Berlin/Heidelberg 37382695 304 10.1140/epje/s10189-023-00304-8 Correction Correction to: Deep reinforcement learning for turbulent drag reduction in channel flows http://orcid.org/0000-0002-8589-1572 Guastoni Luca guastoni@mech.kth.se 12 Rabault Jean jean.rblt@gmail.com 3 Schlatter Philipp pschlatt@mech.kth.se 12 Azizpour Hossein azizpour@kth.se 24 Vinuesa Ricardo rvinuesa@mech.kth.se 12 1 grid.5037.1 0000000121581746 FLOW, Engineering Mechanics, KTH Royal Institute of Technology, 100 44 Stockholm, Sweden 2 grid.512319.d 0000 0005 0274 0966 Swedish E-Science Research Centre (SeRC), 100 44 Stockholm, Sweden 3 grid.82418.37 0000 0001 0226 1499 IT Department, Norwegian Meteorological Institute, Postboks 43, 0313 Oslo, Norway 4 grid.5037.1 0000000121581746 School of Electrical Engineering and Computer Science, KTH Royal Institute of Technology, 100 44 Stockholm, Sweden 29 6 2023 29 6 2023 2023 46 6 51© The Author(s) 2023 https://creativecommons.org/licenses/by/4.0/ 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/. issue-copyright-statement© EDP Sciences, Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2023 ==== Body pmc Correction to : Eur. Phys. J. E (2023) 46:27 https://doi.org/10.1140/epje/s10189-023-00285-8 In this article the annotations have been missing for Fig. 1; the figure should have appeared as shown below. The original article has been corrected.Fig. 1 Overview of our multi-agent DRL approach to drag reduction. The simulation domain is shown on the left. The agents are organized in a grid NCTRLx×NCTRLz. Each agents observes the velocity fluctuations in the streamwise (u′) and wall-normal (v′) direction. The reward is the percentage variation of the wall-shear stress τw. Based on the state, each agent acts by imposing a wall-normal velocity v at the wall