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Description
Neural Operators (NOs) are a deep learning technique designed to learn the solution operator of ordinary and partial differential equations (ODEs and PDEs). Their application to stiff ionic models, which are essential for describing excitable cells in cardiac and neural systems, is a field of growing interest. This study investigates the ability of different NOs architectures to capture the stiff dynamics of the one-dimensional FitzHugh-Nagumo (FHN) model. A key contribution of this work is the evaluation of translation invariance and out-of-distribution generalization. We propose a novel, computationally efficient training strategy in which models are trained using an applied current with varying spatial locations and intensities at a fixed time. These models are then tested on a dataset involving complex translations in both time and space. Furthermore, we conducted a thorough study to evaluate the ability of NOs to learn these translated dynamics and their relative efficiency in terms of training and inference performance.