# Translation Invariance of Neural Operators for the FitzHugh-Nagumo Model

arXiv: https://arxiv.org/abs/2603.17523 · HTML: https://mlsanity.com/paper/2603.17523/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 17 of its 30 references that are in the map.
- First posted on arXiv 18 Mar 2026.

## Builds on (most cited first, 17 of 17)

- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators](https://mlsanity.com/paper/1910.03193/) (2019)
- [DeepXDE: A deep learning library for solving differential equations](https://mlsanity.com/paper/1907.04502/) (2019)
- [Tune: A Research Platform for Distributed Model Selection and Training](https://mlsanity.com/paper/1807.05118/) (2018)
- [Neural Operators for Accelerating Scientific Simulations and Design](https://mlsanity.com/paper/2309.15325/) (2023)
- [A System for Massively Parallel Hyperparameter Tuning](https://mlsanity.com/paper/1810.05934/) (2018)
- [Neural Operators with Localized Integral and Differential Kernels](https://mlsanity.com/paper/2402.16845/) (2024)
- [Nonlocality and Nonlinearity Implies Universality in Operator Learning](https://mlsanity.com/paper/2304.13221/) (2023)
- [A Library for Learning Neural Operators](https://mlsanity.com/paper/2412.10354/) (2024)
- [Learning the Hodgkin-Huxley Model with Operator Learning Techniques](https://mlsanity.com/paper/2406.02173/) (2024)
- [Splitting physics-informed neural networks for inferring the dynamics of integer- and fractional-order neuron models](https://mlsanity.com/paper/2304.13205/) (2023)
- [HyperNOs: Automated and Parallel Library for Neural Operators Research](https://mlsanity.com/paper/2503.18087/) (2025)
- [Physics-informed neural network estimation of active material properties in time-dependent cardiac biomechanical models](https://mlsanity.com/paper/2505.03382/) (2025)
- [Learning High-dimensional Ionic Model Dynamics Using Fourier Neural Operators](https://mlsanity.com/paper/2505.14039/) (2025)
- [NOBLE -- Neural Operator with Biologically-informed Latent Embeddings to Capture Experimental Variability in Biological Neuron Models](https://mlsanity.com/paper/2506.04536/) (2025)
- [Learning cardiac activation and repolarization times with operator learning](https://mlsanity.com/paper/2505.08631/) (2025)

## Abstract (arXiv)

Neural operators (NOs) are powerful deep learning frameworks designed to learn solution operators of partial differential equations. This study evaluates the ability of NOs' to capture the stiff spatio-temporal dynamics of the FitzHugh-Nagumo model. A key contribution of this study is the assessment of the translation invariance using a novel training strategy. Models are trained using an applied current with varying spatial locations and intensities at a fixed time, while the test set presents a challenging out-of-distribution scenario where the current is translated in both time and space. This approach significantly reduces dataset generation costs. We benchmark seven NO architectures: Convolutional Neural Operators (CNOs), Deep Operator Networks (DeepONets), DeepONets with CNN encoders, Proper Orthogonal Decomposition DeepONets, Fourier Neural Operators (FNOs), Tucker Tensorized FNOs, and Local Neural Operators. We evaluated these models based on their accuracy, efficiency, and inference speed. These results demonstrate that CNOs generalize well to translated test dynamics, whereas other architectures do not generalize well. On the training set, all architectures achieve comparable accuracy, with FNOs achieving the highest precision. However, this higher accuracy comes at an elevated computational cost. Meanwhile, DeepONets and their variants exhibit superior training and inference efficiency. These findings highlight the capabilities and limitations of NOs in modeling complex ionic dynamics and provide a comprehensive benchmark for scenarios involving translated dynamics.