We propose, in this paper, a Variable Spiking Wavelet Neural Operator (VS-WNO), which aims to bridge the gap between theoretical and practical implementation of Artificial Intelligence (AI) algorithms for mechanics applications. With recent developments like the introduction of neural operators, AI's potential for being used in mechanics applications has increased significantly. However, AI's immense energy and resource requirements are a hurdle in its practical field use case. The proposed VS-WNO is based on the principles of spiking neural networks, which have shown promise in reducing the energy requirements of the neural networks. This makes possible the use of such algorithms in edge computing. The proposed VS-WNO utilizes variable spiking neurons, which promote sparse communication, thus conserving energy, and its use is further supported by its ability to tackle regression tasks, often faced in the field of mechanics. Various examples dealing with partial differential equations, like Burger's equation, Allen Cahn's equation, and Darcy's equation, have been shown. Comparisons have been shown against wavelet neural operator utilizing leaky integrate and fire neurons (direct and encoded inputs) and vanilla wavelet neural operator utilizing artificial neurons. The results produced illustrate the ability of the proposed VS-WNO to converge to ground truth while promoting sparse communication.

翻译：本文提出了一种变分脉冲小波神经算子（VS-WNO），旨在弥合力学应用中人工智能（AI）算法的理论设计与实际部署之间的鸿沟。随着神经算子等最新进展的引入，AI在力学应用中的潜力显著提升。然而，AI巨大的能耗和资源需求仍是其实际现场应用的障碍。所提出的VS-WNO基于脉冲神经网络原理，这类网络已被证明能降低神经网络的能耗，从而使得此类算法在边缘计算中的应用成为可能。VS-WNO采用变分脉冲神经元，通过促进稀疏通信来节约能量，并且其对力学领域常见回归任务的适用性进一步支持了其应用。文中展示了多个涉及偏微分方程的示例，如伯格斯方程、艾伦-卡恩方程和达西方程。通过对比基于泄漏积分-点火神经元（直接输入与编码输入）的小波神经算子以及采用人工神经元的原始小波神经算子，实验结果证明VS-WNO能够在保持稀疏通信的同时收敛至真实解。