Training machine learning models for radioisotope identification using gamma spectroscopy remains an elusive challenge for many practical applications, largely stemming from the difficulty of acquiring and labeling large, diverse experimental datasets. Simulations can mitigate this challenge, but the accuracy of models trained on simulated data can deteriorate substantially when deployed to an out-of-distribution operational environment. In this study, we demonstrate that unsupervised domain adaptation (UDA) can improve the ability of a model trained on synthetic data to generalize to a new testing domain, provided unlabeled data from the target domain is available. Conventional supervised techniques are unable to utilize this data because the absence of isotope labels precludes defining a supervised classification loss. We compare a range of different UDA techniques, finding that feature alignment strategies, particularly via maximum mean discrepancy (MMD) minimization or domain-adversarial training, yield the most consistent improvement to testing scores. For instance, using a custom transformer-based neural network, we achieve a testing accuracy of $0.904 \pm 0.022$ on an experimental LaBr$_3$ test set after performing unsupervised feature alignment via MMD minimization, compared to $0.754 \pm 0.014$ before alignment. Overall, our results highlight the potential of using UDA to adapt a radioisotope classifier trained on synthetic data for real-world deployment.

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