# Neuroscience inspired scientific machine learning (Part-2): Variable spiking wavelet neural operator

arXiv: https://arxiv.org/abs/2311.14710 · HTML: https://mlsanity.com/paper/2311.14710/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 40 references that are in the map.
- First posted on arXiv 15 Nov 2023.

## Builds on (most cited first, 15 of 15)

- [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)
- [Surrogate Gradient Learning in Spiking Neural Networks](https://mlsanity.com/paper/1901.09948/) (2019)
- [Training Spiking Neural Networks Using Lessons From Deep Learning](https://mlsanity.com/paper/2109.12894/) (2021)
- [SuperSpike: Supervised learning in multi-layer spiking neural networks](https://mlsanity.com/paper/1705.11146/) (2017)
- [Enabling Deep Spiking Neural Networks with Hybrid Conversion and Spike Timing Dependent Backpropagation](https://mlsanity.com/paper/2005.01807/) (2020)
- [Optimal ANN-SNN Conversion for High-accuracy and Ultra-low-latency Spiking Neural Networks](https://mlsanity.com/paper/2303.04347/) (2023)
- [Event-Based Angular Velocity Regression with Spiking Networks](https://mlsanity.com/paper/2003.02790/) (2020)
- [An Analytical Estimation of Spiking Neural Networks Energy Efficiency](https://mlsanity.com/paper/2210.13107/) (2022)
- [Physics informed WNO](https://mlsanity.com/paper/2302.05925/) (2023)
- [Rate Coding or Direct Coding: Which One is Better for Accurate, Robust, and Energy-efficient Spiking Neural Networks?](https://mlsanity.com/paper/2202.03133/) (2022)
- [Multi-fidelity wavelet neural operator with application to uncertainty quantification](https://mlsanity.com/paper/2208.05606/) (2022)
- [Artificial to Spiking Neural Networks Conversion for Scientific Machine Learning](https://mlsanity.com/paper/2308.16372/) (2023)
- [SMS: Spiking Marching Scheme for Efficient Long Time Integration of Differential Equations](https://mlsanity.com/paper/2211.09928/) (2022)
- [Waveformer for modelling dynamical systems](https://mlsanity.com/paper/2310.04990/) (2023)

## Built on by (most cited first, 1 of 1)

- [Real-Time Sensing of Inaccessible Physical Fields via an Edge-Deployable Hardware-Portable Graph Neural Operator](https://mlsanity.com/paper/2604.01802/) (2026)

## Abstract (arXiv)

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.