Biophysics-informed deep operator learning for inverse problems with application to electrophysiological source reconstruction

2026-08-17

AI Summary

This study addresses the ill-posedness, noise sensitivity, and poor cross-subject generalization inherent in magnetoencephalography (MEG) source reconstruction by proposing a biophysically-informed deep operator learning framework. By integrating differentiable physics layers with geometric deep operator networks, this approach embeds sensing mechanisms directly into the model to enable efficient neural source reconstruction and individualized anatomical adaptation. Experiments on both simulated and real auditory evoked data demonstrate that the proposed method significantly reduces reconstruction errors while yielding anatomically plausible cortical activation localization. Furthermore, it effectively enhances data efficiency and cross-subject generalizability, establishing a novel paradigm for precise brain functional imaging.

Abstract

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.

Problem

• Electrophysiological source reconstruction
• Inverse problems
• Biophysics-informed learning
• Subject-specific adaptation
• Ill-posedness

Innovation

• Biophysics-informed
• Deep operator learning
• Differentiable layer
• Source reconstruction
• Inverse problems