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Neural coupling is a fundamental mechanism in neuroscience that facilitates the emergence of cognitive functions through dynamic interactions and synchronization among distributed brain regions. Inspired by this principle, we pose the question: Might the biological mechanism of neural oscillatory synchronization inspire the feature representation learning for neuroscience? By addressing this question through the Kuramoto model, renowned for simulating oscillatory dynamics, we present a novel physics-informed deep model, `SyncBrain`, it models brain regions as interacting oscillatory units and simulates their temporal dynamics and synchronization patterns to distinguish cognitive states. Furthermore, inspired by the brain's inherent ability to dynamically attend to critical temporal information, we incorporate an adaptive control module that introduces an attention-like mechanism to guide information flow. We evaluate our model on multiple functional neuroimaging datasets, it demonstrates promising performance and enhanced interpretability in both cognitive state decoding and early disease diagnosis, outperforming existing computational methods. These results demonstrate the effectiveness of neural oscillatory mechanisms in shaping robust and interpretable machine learning models for neuroscience applications.