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Machine Learning is used in this paper for noise-diagnostics to detect defined anomalies in nuclear plant reactor cores solely from neutron detector measurements. The proposed approach leverages advanced diffusion-based core simulation tools to generate large amounts of simulated data with different types of driving perturbations originating at all theoretically possible locations in the core. Specifically the CORE SIM+ modelling framework is employed, which generates these data in the frequency domain. We train using these vast quantities of simulated data state-of-the-art machine and deep learning models which are used to successfully perform semantic segmentation, classification and localisation of multiple simultaneously occurring in-core perturbations. Actual plant data are then considered, provided by two different reactors, including no labels about perturbation existence. A domain adaptation methodology is subsequently developed to extend the simulated setting to real plant measurements, which uses self-supervised, or unsupervised learning, to align the simulated data with the actual plant data and detect perturbations, whilst classifying their type and estimating their location. Experimental studies illustrate the successful performance of the developed approach and extensions are described that indicate a great potential for further research.