Electrophysiological brain signals are typically acquired through indirect and noisy measurements, providing transformed representations of the underlying neural activity. Source reconstruction---the inverse problem of resolving underlying neural signals from these measurements---is essential for mapping brain function but remains challenging because it is ill-posed and sensitive to noise. Deep learning methods have shown promise across a range of inverse problems, yet many do not explicitly incorporate the biophysical principles governing data generation, limiting data efficiency and adaptation across subjects. Here, we introduce DeepOp-Informed, a biophysics-informed geometric deep operator learning framework that embeds the biophysics of the sensing process into the model through a custom differentiable layer, enabling more efficient learning and improved reconstruction performance. This layer enables the neural network to adapt to subject-specific variations in the physics of signal generation, resulting from differences in brain anatomy and sensor positioning. In realistic magnetoencephalography simulations, DeepOp-Informed generalizes to forward models from held-out subjects, reducing reconstruction error relative to several neural-network and classical baselines. Applied to adolescent auditory-evoked recordings, it produces anatomically plausible reconstructions localized to the auditory cortex. While our application focuses on magnetoencephalography, the framework is general and may be adaptable to other imaging modalities.
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