  To facilitate a wide-spread acceptance of AI systems guiding decision making
in real-world applications, trustworthiness of deployed models is key. That is,
it is crucial for predictive models to be uncertainty-aware and yield
well-calibrated (and thus trustworthy) predictions for both in-domain samples
as well as under domain shift. Recent efforts to account for predictive
uncertainty include post-processing steps for trained neural networks, Bayesian
neural networks as well as alternative non-Bayesian approaches such as ensemble
approaches and evidential deep learning. Here, we propose an efficient yet
general modelling approach for obtaining well-calibrated, trustworthy
probabilities for samples obtained after a domain shift. We introduce a new
training strategy combining an entropy-encouraging loss term with an
adversarial calibration loss term and demonstrate that this results in
well-calibrated and technically trustworthy predictions for a wide range of
domain drifts. We comprehensively evaluate previously proposed approaches on
different data modalities, a large range of data sets including sequence data,
network architectures and perturbation strategies. We observe that our
modelling approach substantially outperforms existing state-of-the-art
approaches, yielding well-calibrated predictions under domain drift.
