We propose a challenge organised in conjunction with the Fair Universe project, a collaborative effort funded by the US Department of Energy and involving the Lawrence Berkeley National Laboratory, Université Paris-Saclay, University of Washington, and ChaLearn. This initiative aims to forge an open AI ecosystem for scientific discovery. The challenge will focus on measuring the physics properties of elementary particles with imperfect simulators due to differences in modelling systematic errors. Additionally, the challenge will leverage a large-compute-scale AI platform for sharing datasets, training models, and hosting machine learning competitions. Our challenge will bring together the physics and machine learning communities to advance our understanding and methodologies in handling systematic (otherwise known as epistemic) uncertainties within AI techniques.