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Fast Surrogate Modeling of Excitable and Oscillatory FitzHugh-Nagumo Dynamics with Parametric Neural Operators

arXiv · AI, language, vision and robotics · article · Sep 3, 2026 · UTC

The FitzHugh-Nagumo (FHN) system serves as a simplified model of neuronal voltage dynamics, capturing the activator-inhibitor structure behind both isolated action potentials and the rhythmic spiking seen across the brain. Exploring its 5D physiological parameter space is important for neuromodulation and mapping voltage recordings back to biophysics, yet classical finite-difference solvers make rapid parameter sweeps expensive. We train parameter-conditioned Fourier Neural Operators (FNOs) as fast, differentiable surrogates for the FHN voltage and recovery fields on a one-dimensional spatial

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