Metal additive manufacturing (AM) offers significant opportunities for flexible, efficient, and cost-effective printing of highly complex parts. Despite recent successes, metal AM is still limited to relatively few alloys. In order to qualify new alloys for metal AM, process parameters must be optimised to produce high-quality and consistent components. However, process parameter optimisation is often a challenging and cost-prohibitive task. In this work, we propose a novel, deep learning-based approach that allows for fast, high-quality, non-destructive characterisation of AM parts from sparse X-ray computed tomography (CT) measurements. The proposed approach rapidly produces high-quality reconstructions from fast X-ray CT scans of metal AM parts by leveraging digital models of the component and physics-based simulations of nonlinear interactions between X-ray radiation and metals, significantly reducing beam hardening, metal, and other common X-ray CT artifacts. The method allows for batch characterisation of hundreds of AM parts printed on the same plate with different printing parameters, paving the way for identifying the optimum printing parameters for new AM materials. We present results for an experimental case study illustrating the practical utility of our method. The proposed approach not only produced accurate 3D volumetric reconstruction images of the parts from their respective sparsely measured X-ray CT scans but also resulted in both a 300% reduction in total scan time and more than 4X improvement in probability of flaw detection in post-processing analysis of the data. This has enabled us to rapidly search for and identify useful process parameters that can lead to high-quality parts made from a novel AlCe alloy.