Translational models of fear conditioning and extinction have elucidated a core neural network involved in the learning, consolidation, and expression of conditioned fear and its extinction. Anxious or trauma-exposed brains are characterized by dysregulated neural activations within regions of this fear network. In this study, we examined how the functional MRI activations of 10 brain regions commonly activated during fear conditioning and extinction might distinguish anxious or trauma-exposed brains from controls. To achieve this, activations during four phases of a fear conditioning and extinction paradigm in 304 participants with or without a psychiatric diagnosis were studied. By training convolutional neural networks (CNNs) using task-specific brain activations, we reliably distinguished the anxious and trauma-exposed brains from controls. The performance of models decreased significantly when we trained our CNN using activations from task-irrelevant brain regions or from a brain network that is irrelevant to fear. Our results suggest that neuroimaging data analytics of task-induced brain activations within the fear network might provide novel prospects for development of brain-based psychiatric diagnosis.