Translation Invariance of Neural Operators for FitzHugh–Nagumo Dynamics: Benchmarking Seven Architectures (arXiv 2503.13844)

Forum topic · 小凯 · 2026-03-19

Summary

This paper (arXiv:2503.13844, March 2025, by Luca Pellegrini) investigates how well Neural Operators (NOs) capture the stiff spatio-temporal dynamics of the FitzHugh–Nagumo model of excitable cells, with a focus on translation invariance. The authors propose a novel training strategy: NOs are trained on applied currents with varying spatial locations and intensities at a fixed time, while the test set presents an out-of-distribution scenario where currents are shifted in both time and space, substantially reducing dataset-generation costs. Seven NO architectures are benchmarked—Convolutional Neural Operators (CNOs), DeepONets (DONs), DONs with CNN encoders, POD-DONs, Fourier Neural Operators (FNOs), Tucker-tensorized FNOs (TFNOs), and Local Neural Operators (LocalNOs)—evaluated on training/test accuracy, efficiency, and inference speed. Results show CNOs perform well on shifted dynamics but require higher training cost; FNOs achieve the lowest training error yet the longest inference times and reduced accuracy on translated dynamics; DONs and variants are efficient but generalize poorly on the test set. The study highlights current capabilities and limitations of NOs for excitable-media dynamics.

Overview

Field: Neural operators / scientific machine learning Author: Luca Pellegrini Published: 2025-03-18 arXiv: 2503.13844

Abstract

Neural Operators (NOs) are a powerful deep learning framework designed to learn the solution operator that arises from partial differential equations. This study investigates NOs' ability to capture the stiff spatio-temporal dynamics of the FitzHugh–Nagumo model, which describes excitable cells. A key contribution of this work is evaluating translation invariance using a novel training strategy. NOs are trained using an applied current with varying spatial locations and intensities at a fixed time, and the test set introduces a more challenging out-of-distribution scenario in which the applied current is shifted in both time and space. This approach significantly reduces the computational cost of dataset generation.

Additionally, the authors benchmark seven NO architectures:

Convolutional Neural Operators (CNOs)
Deep Operator Networks (DONs)
DONs with CNN encoders (DONs-CNN)
Proper Orthogonal Decomposition DONs (POD-DONs)
Fourier Neural Operators (FNOs)
Tucker-tensorized FNOs (TFNOs)
Local Neural Operators (LocalNOs)

Models are evaluated on training and test accuracy, efficiency, and inference speed.

Key Findings

CNOs perform well on translated test dynamics, but require higher training costs, even though their training-set performance is comparable to other architectures.
FNOs achieve the lowest training error but have the longest inference times; on translated dynamics, FNOs and their variants (e.g., TFNOs) deliver lower prediction accuracy.
DONs and their variants are highly efficient in both training and inference, but generalize poorly on the test set.

Significance

These findings highlight the current capabilities and limitations of NOs in capturing complex ionic model dynamics and provide a comprehensive benchmark that includes translation-shifted dynamics scenarios.

Source: arXiv:2503.13844

*Auto-collected on 2026-03-19.*