Green's Neural Operator with Neumann conditions for EMG volume conductor modelling

Noura Ezaz-Nikpay, Dimitrios Halatsis, Dario Farina

Keywords: neural operator, green's function, EMG simulation

Abstract: Simulating electromyography (EMG) signals has a computational bottleneck: repeatedly solving the anisotropic Poisson equation on patient-specific volume conductor geometries. We learn a Green's function representation using a latent neural operator (LNO), extending prior neural Green's approaches from Dirichlet to Neumann boundary conditions. In 5-fold cross-validation over held-out geometry-conductivity configurations, the Green's formulation outperforms a FiLM-conditioned standard LNO formulation with fewer parameters and 2.5$\times$ lower variance. However, spatial holdout experiments reveal a vulnerability of the Green's formulation: when entire regions are devoid of training sources, the Green's model fails. We trace this to asymmetric gradient flow through the learned eigenfunctions and show that the failure does not occur when training sources have adequate spatial coverage. These findings delineate when the Green's formulation offers advantages over direct prediction approaches. This workshop paper is a proof of concept; future work will investigate more complex anatomies.

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Submission Number: 136