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To control the temporal profile of a relativistic electron beam to meetrequirements of various advanced scientific applications likefree-electron-laser and plasma wakefield acceleration, a widely-used techniqueis to manipulate the dispersion terms which turns out to be one-to-manyproblems. Due to their intrinsic one-to-many property, current popularstochastic optimization approaches on temporal shaping may face the problems oflong computing time or sometimes suggesting only one solution. Here we proposea real-time solver for one-to-many problems of temporal shaping, with the aidof a semi-supervised machine learning method, the conditional generativeadversarial network (CGAN). We demonstrate that the CGAN solver can learn theone-to-many dynamics and is able to accurately and quickly predict the requireddispersion terms for different custom temporal profiles. This machinelearning-based solver is expected to have the potential for wide applicationsto one-to-many problems in other scientific fields.

Machine learning-based direct solver for one-to-many problems on temporal shaping of relativistic electron beams