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One remedy is to integrate in a parallel fashion, \u201cpredicting\u201d the solution serially using a cheap (coarse) solver and \u201ccorrecting\u201d these values using an expensive (fine) solver that runs in parallel on a number of temporal subintervals. In this work, we propose a time-parallel algorithm (<jats:italic>GParareal<\/jats:italic>) that solves IVPs by modelling the correction term, i.e. the difference between fine and coarse solutions, using a Gaussian process emulator. This approach compares favourably with the classic<jats:italic>parareal<\/jats:italic>algorithm and we demonstrate, on a number of IVPs, that GParareal can converge in fewer iterations than parareal, leading to an increase in parallel speed-up. GParareal also manages to locate solutions to certain IVPs where parareal fails and has the additional advantage of being able to use archives of legacy solutions, e.g. solutions from prior runs of the IVP for different initial conditions, to further accelerate convergence of the method \u2014 something that existing time-parallel methods do not do.<\/jats:p>","DOI":"10.1007\/s11222-022-10195-y","type":"journal-article","created":{"date-parts":[[2022,12,21]],"date-time":"2022-12-21T21:02:56Z","timestamp":1671656576000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["GParareal: a time-parallel ODE solver using Gaussian process emulation"],"prefix":"10.1007","volume":"33","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9530-1890","authenticated-orcid":false,"given":"Kamran","family":"Pentland","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Massimiliano","family":"Tamborrino","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"T. 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