From LIF to QIF: Toward Differentiable Spiking Neurons for Scientific Machine Learning

TL;DR

This paper introduces Quadratic Integrate-and-Fire neurons with differentiable dynamics, enabling effective gradient-based training of spiking neural networks for scientific machine learning tasks, outperforming traditional models.

Contribution

It presents the QIF neuron as a novel, differentiable spiking model that improves training stability and accuracy in SNNs for scientific computing applications.

Findings

QIF neurons enable gradient-based training of SNNs.

QIF-based models outperform LIF in accuracy and stability.

QIF improves function approximation and PDE solving in benchmarks.

Abstract

Spiking neural networks (SNNs) offer biologically inspired computation but remain underexplored for continuous regression tasks in scientific machine learning. In this work, we introduce and systematically evaluate Quadratic Integrate-and-Fire (QIF) neurons as an alternative to the conventional Leaky Integrate-and-Fire (LIF) model in both directly trained SNNs and ANN-to-SNN conversion frameworks. The QIF neuron exhibits smooth and differentiable spiking dynamics, enabling gradient-based training and stable optimization within architectures such as multilayer perceptrons (MLPs), Deep Operator Networks (DeepONets), and Physics-Informed Neural Networks (PINNs). Across benchmarks on function approximation, operator learning, and partial differential equation (PDE) solving, QIF-based networks yield smoother, more accurate, and more stable predictions than their LIF counterparts, which suffer from discontinuous time-step responses and jagged activation surfaces. These results position the QIF neuron as a computational bridge between spiking and continuous-valued deep learning, advancing the integration of neuroscience-inspired dynamics into physics-informed and operator-learning frameworks.