We are grateful to E. Feibush from the US Department of Energy (DOE) Princeton Plasma Physics Laboratory (PPPL) and the Princeton Institute for Computational Science and Engineering (PICSciE) for assisting with visualization and data collection; to W. Wichser, C. Hillegas, J. Wells, S. Matsuoka, R. Yokota and T. Gibbs for supporting our supercomputing efforts; to T. Donne for facilitating collaborations with JET; to E. Joffrin, R. Buttery and T. Strait for leading the internal reviews of this work at JET and DIII-D; to A. Murari, J. Vega and the associated JET data analysis team for discussions of their classical machine-learning methods; and to M. Maslov for support with the JET data. We also thank R. Nazikian, N. Logan, M. Parsons and M. Churchill of PPPL; K. Felker of Princeton University; R. Granetz and C. Rea of the Massachusetts Institute of Technology (MIT); and P. DeVries of ITER for support and for discussions. We thank the JET contributors35 and management as well as General Atomics (GA) and its DIII-D tokamak project for access to their fusion databases. J.K.-H. was supported by the DOE Computational Science Graduate Fellowship Program of the Office of Science and National Nuclear Security Administration in the DOE under contract DE-FG02-97ER25308. A.S. is supported by PICSciE, and W.T. by PPPL and PICSciE. This work was carried out within the framework of the EUROfusion Consortium, with funding from the Euratom research and training programme 2014–2018 under grant 633053. The views and opinions expressed herein do not necessarily reflect those of the European Commission. This material is based upon work supported by the US DOE, Office of Science, Office of Fusion Energy Sciences, using the DIII-D National Fusion Facility, a DOE Office of Science user facility, under award DE-FC02-04ER54698. Disclaimer: this report was prepared as an account of work sponsored by an agency of the US Government. Neither the US Government nor any agency thereof, nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recommendation, or favoring by the US Government or any agency thereof. The views and opinions of authors expressed herein do not necessarily state or reflect those of the US Government or any agency thereof.

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Nature thanks Ned R. Sauthoff and the other anonymous reviewer(s) for their contribution to the peer review of this work.