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Due to the dynamic cortical development of neonates after birth, existing cortical surface atlases for adults are not suitable for representing neonatal brains. It has been proposed that pediatric spatio-temporal atlases are more appropriate to characterize the neural development. We present a novel network comprised of an atlas inference module and a non-linear surface registration module, SphereMorph, to construct a continuous neonatal cortical surface atlas with respect to post-menstrual age. We explicitly aim to diminish bias in the constructed atlas by regularizing the mean displacement field. We trained the network on 445 neonatal cortical surfaces from the developing Human Connectome Project (dHCP). We assessed the quality of the constructed atlas by evaluating the accuracy of the spatial normalization of another 100 dHCP surfaces as well as the parcellation accuracy of 10 subjects from an …