  The Euclid Space Telescope will provide deep imaging at optical and
near-infrared wavelengths, along with slitless near-infrared spectroscopy,
across ~15,000 sq deg of the sky. Euclid is expected to detect ~12 billion
astronomical sources, facilitating new insights into cosmology, galaxy
evolution, and various other topics. To optimally exploit the expected very
large data set, there is the need to develop appropriate methods and software.
Here we present a novel machine-learning based methodology for selection of
quiescent galaxies using broad-band Euclid I_E, Y_E, J_E, H_E photometry, in
combination with multiwavelength photometry from other surveys. The ARIADNE
pipeline uses meta-learning to fuse decision-tree ensembles,
nearest-neighbours, and deep-learning methods into a single classifier that
yields significantly higher accuracy than any of the individual learning
methods separately. The pipeline has `sparsity-awareness', so that missing
photometry values are still informative for the classification. Our pipeline
derives photometric redshifts for galaxies selected as quiescent, aided by the
`pseudo-labelling' semi-supervised method. After application of the outlier
filter, our pipeline achieves a normalized mean absolute deviation of ~< 0.03
and a fraction of catastrophic outliers of ~< 0.02 when measured against the
COSMOS2015 photometric redshifts. We apply our classification pipeline to mock
galaxy photometry catalogues corresponding to three main scenarios: (i) Euclid
Deep Survey with ancillary ugriz, WISE, and radio data; (ii) Euclid Wide Survey
with ancillary ugriz, WISE, and radio data; (iii) Euclid Wide Survey only. Our
classification pipeline outperforms UVJ selection, in addition to the Euclid
I_E-Y_E, J_E-H_E and u-I_E,I_E-J_E colour-colour methods, with improvements in
completeness and the F1-score of up to a factor of 2. (Abridged)
