Particle accelerators are enabling tools for scientific exploration and
discovery in various disciplines. Finding optimized operation points for these
complex machines is a challenging task, however, due to the large number of
parameters involved and the underlying non-linear dynamics. Here, we introduce
two families of data-driven surrogate models, based on deep and invertible
neural networks, that can replace the expensive physics computer models. These
models are employed in multi-objective optimisations to find Pareto optimal
operation points for two fundamentally different types of particle
accelerators. Our approach reduces the time-to-solution for a multi-objective
accelerator optimisation up to a factor of 640 and the computational cost up to
98%. The framework established here should pave the way for future on-line and
real-time multi-objective optimisation of particle accelerators
