# Spiking Neural Operators for Scientific Machine Learning

arXiv: https://arxiv.org/abs/2205.10130 · HTML: https://mlsanity.com/paper/2205.10130/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 46 references that are in the map.
- First posted on arXiv 17 May 2022.

## Builds on (most cited first, 14 of 14)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators](https://mlsanity.com/paper/1910.03193/) (2019)
- [Provably Efficient Reinforcement Learning with Linear Function Approximation](https://mlsanity.com/paper/1907.05388/) (2019)
- [Physics-informed neural networks (PINNs) for fluid mechanics: A review](https://mlsanity.com/paper/2105.09506/) (2021)
- [Deep Learning in Spiking Neural Networks](https://mlsanity.com/paper/1804.08150/) (2018)
- [Training Spiking Neural Networks Using Lessons From Deep Learning](https://mlsanity.com/paper/2109.12894/) (2021)
- [Going Deeper in Spiking Neural Networks: VGG and Residual Architectures](https://mlsanity.com/paper/1802.02627/) (2018)
- [Training Deep Spiking Neural Networks using Backpropagation](https://mlsanity.com/paper/1608.08782/) (2016)
- [Multifidelity deep neural operators for efficient learning of partial differential equations with application to fast inverse design of nanoscale heat transport](https://mlsanity.com/paper/2204.06684/) (2022)
- [Revisiting Batch Normalization for Training Low-latency Deep Spiking Neural Networks from Scratch](https://mlsanity.com/paper/2010.01729/) (2020)
- [Physics-informed neural network for ultrasound nondestructive quantification of surface breaking cracks](https://mlsanity.com/paper/2005.03596/) (2020)
- [An Ensemble of Simple Convolutional Neural Network Models for MNIST Digit Recognition](https://mlsanity.com/paper/2008.10400/) (2020)
- [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)
- [Neural-net-induced Gaussian process regression for function approximation and PDE solution](https://mlsanity.com/paper/1806.11187/) (2018)

## Built on by (most cited first, 8 of 8)

- [Spiking neural networks for nonlinear regression](https://mlsanity.com/paper/2210.03515/) (2022)
- [Learning the Hodgkin-Huxley Model with Operator Learning Techniques](https://mlsanity.com/paper/2406.02173/) (2024)
- [SMS: Spiking Marching Scheme for Efficient Long Time Integration of Differential Equations](https://mlsanity.com/paper/2211.09928/) (2022)
- [Hybrid variable spiking graph neural networks for energy-efficient scientific machine learning](https://mlsanity.com/paper/2412.09379/) (2024)
- [Distribution free uncertainty quantification in neuroscience-inspired deep operators](https://mlsanity.com/paper/2412.09369/) (2024)
- [SCNO: Spiking Compositional Neural Operator -- Towards a Neuromorphic Foundation Model for Nuclear PDE Solving](https://mlsanity.com/paper/2604.11625/) (2026)
- [Neural Network Modeling of Microstructure Complexity Using Digital Libraries](https://mlsanity.com/paper/2501.18189/) (2025)
- [Operator Learning for Reconstructing Flow Fields from Sparse Measurements: a Language Model Approach](https://mlsanity.com/paper/2605.23712/) (2026)

## Abstract (arXiv)

The main computational task of Scientific Machine Learning (SciML) is function regression, required both for inputs as well as outputs of a simulation. Physics-Informed Neural Networks (PINNs) and neural operators (such as DeepONet) have been very effective in solving Partial Differential Equations (PDEs), but they tax computational resources heavily and cannot be readily adopted for edge computing. Here, we address this issue by considering Spiking Neural Networks (SNNs), which have shown promise in reducing energy consumption by two orders of magnitude or more. We present a SNN-based method to perform regression, which has been a challenge due to the inherent difficulty in representing a function's input domain and continuous output values as spikes. We first propose a new method for encoding continuous values into spikes based on a triangular matrix in space and time, and demonstrate its better performance compared to the existing methods. Next, we demonstrate that using a simple SNN architecture consisting of Leaky Integrate and Fire (LIF) activation and two dense layers, we can achieve relatively accurate function regression results. Moreover, we can replace the LIF with a trained Multi-Layer Perceptron (MLP) network and obtain comparable results but three times faster. Then, we introduce the DeepONet, consisting of a branch (typically a Fully-connected Neural Network, FNN) for inputs and a trunk (also a FNN) for outputs. We can build a spiking DeepONet by either replacing the branch or the trunk by a SNN. We demonstrate this new approach for classification using the SNN in the branch, achieving results comparable to the literature. Finally, we design a spiking DeepONet for regression by replacing its trunk with a SNN, and achieve good accuracy for approximating functions as well as inferring solutions of differential equations.