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.

翻译：脉冲神经网络（SNNs）提供了受生物学启发的计算范式，但在科学机器学习中的连续回归任务方面仍未得到充分探索。本研究引入并系统评估了二次积分发放（QIF）神经元，作为传统泄漏积分发放（LIF）模型在直接训练的SNNs和ANN-to-SNN转换框架中的替代方案。QIF神经元展现出平滑且可微分的脉冲动力学特性，能够在多层感知机（MLPs）、深度算子网络（DeepONets）和物理信息神经网络（PINNs）等架构中实现基于梯度的训练和稳定优化。在函数逼近、算子学习和偏微分方程（PDE）求解的基准测试中，基于QIF的网络比LIF网络产生更平滑、更准确且更稳定的预测结果，而后者存在离散时间步响应不连续和激活曲面不平整的问题。这些结果表明，QIF神经元可作为脉冲计算与连续值深度学习之间的计算桥梁，推动神经科学启发的动力学机制与物理信息及算子学习框架的进一步融合。