  We review research at the National Physical Laboratory (NPL) in the area of
trustworthy artificial intelligence (TAI), and more specifically trustworthy
machine learning (TML), in the context of metrology, the science of
measurement. We describe three broad themes of TAI: technical, socio-technical
and social, which play key roles in ensuring that the developed models are
trustworthy and can be relied upon to make responsible decisions. From a
metrology perspective we emphasise uncertainty quantification (UQ), and its
importance within the framework of TAI to enhance transparency and trust in the
outputs of AI systems. We then discuss three research areas within TAI that we
are working on at NPL, and examine the certification of AI systems in terms of
adherence to the characteristics of TAI.
