# Spiking neural networks for nonlinear regression

arXiv: https://arxiv.org/abs/2210.03515 · HTML: https://mlsanity.com/paper/2210.03515/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Builds on 39 of its 123 references that are in the map.
- First posted on arXiv 6 Oct 2022.

## Builds on (most cited first, 30 of 39)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [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)
- [Physics-informed neural networks (PINNs) for fluid mechanics: A review](https://mlsanity.com/paper/2105.09506/) (2021)
- [Incorporating Learnable Membrane Time Constant to Enhance Learning of Spiking Neural Networks](https://mlsanity.com/paper/2007.05785/) (2020)
- [Deep Residual Learning in Spiking Neural Networks](https://mlsanity.com/paper/2102.04159/) (2021)
- [SLAYER: Spike Layer Error Reassignment in Time](https://mlsanity.com/paper/1810.08646/) (2018)
- [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)
- [SuperSpike: Supervised learning in multi-layer spiking neural networks](https://mlsanity.com/paper/1705.11146/) (2017)
- [Long short-term memory and learning-to-learn in networks of spiking neurons](https://mlsanity.com/paper/1803.09574/) (2018)
- [Efficient Neuromorphic Signal Processing with Loihi 2](https://mlsanity.com/paper/2111.03746/) (2021)
- [The Modern Mathematics of Deep Learning](https://mlsanity.com/paper/2105.04026/) (2021)
- [Memory and information processing in neuromorphic systems](https://mlsanity.com/paper/1506.03264/) (2015)
- [Physics-Informed Neural Network for Modelling the Thermochemical Curing Process of Composite-Tool Systems During Manufacture](https://mlsanity.com/paper/2011.13511/) (2020)
- [Progressive Tandem Learning for Pattern Recognition with Deep Spiking Neural Networks](https://mlsanity.com/paper/2007.01204/) (2020)
- [Physics informed neural networks for continuum micromechanics](https://mlsanity.com/paper/2110.07374/) (2021)
- [Event-Based Angular Velocity Regression with Spiking Networks](https://mlsanity.com/paper/2003.02790/) (2020)
- [Sparse Spiking Gradient Descent](https://mlsanity.com/paper/2105.08810/) (2021)
- [Physics-Informed Neural Networks for Nonhomogeneous Material Identification in Elasticity Imaging](https://mlsanity.com/paper/2009.04525/) (2020)
- [Optimizing the energy consumption of spiking neural networks for neuromorphic applications](https://mlsanity.com/paper/1912.01268/) (2019)
- [Reconstruction of three-dimensional porous media using generative adversarial neural networks](https://mlsanity.com/paper/1704.03225/) (2017)
- [ReckOn: A 28nm Sub-mm2 Task-Agnostic Spiking Recurrent Neural Network Processor Enabling On-Chip Learning over Second-Long Timescales](https://mlsanity.com/paper/2208.09759/) (2022)
- [Hardware Implementation of Deep Network Accelerators Towards Healthcare and Biomedical Applications](https://mlsanity.com/paper/2007.05657/) (2020)
- [A Long Short-Term Memory for AI Applications in Spike-based Neuromorphic Hardware](https://mlsanity.com/paper/2107.03992/) (2021)
- [NN-EUCLID: deep-learning hyperelasticity without stress data](https://mlsanity.com/paper/2205.06664/) (2022)
- [Meshless physics-informed deep learning method for three-dimensional solid mechanics](https://mlsanity.com/paper/2012.01547/) (2020)
- [A Spiking Neural Network for Image Segmentation](https://mlsanity.com/paper/2106.08921/) (2021)
- [A machine learning based plasticity model using proper orthogonal decomposition](https://mlsanity.com/paper/2001.03438/) (2020)
- [Stress Field Prediction in Cantilevered Structures Using Convolutional Neural Networks](https://mlsanity.com/paper/1808.08914/) (2018)

## Built on by (most cited first, 10 of 10)

- [Deep Learning in Deterministic Computational Mechanics](https://mlsanity.com/paper/2309.15421/) (2023)
- [Autonomous Driving with Spiking Neural Networks](https://mlsanity.com/paper/2405.19687/) (2024)
- [Learning solution of nonlinear constitutive material models using physics-informed neural networks: COMM-PINN](https://mlsanity.com/paper/2304.06044/) (2023)
- [Time to Spike? Understanding the Representational Power of Spiking Neural Networks in Discrete Time](https://mlsanity.com/paper/2505.18023/) (2025)
- [Hybrid variable spiking graph neural networks for energy-efficient scientific machine learning](https://mlsanity.com/paper/2412.09379/) (2024)
- [Underwater Image Enhancement by Convolutional Spiking Neural Networks](https://mlsanity.com/paper/2503.20485/) (2025)
- [SQUAT: Stateful Quantization-Aware Training in Recurrent Spiking Neural Networks](https://mlsanity.com/paper/2404.19668/) (2024)
- [Hardware-aware vs. Hardware-agnostic Energy Estimation for SNN in Space Applications](https://mlsanity.com/paper/2508.19654/) (2025)
- [Neural Network Modeling of Microstructure Complexity Using Digital Libraries](https://mlsanity.com/paper/2501.18189/) (2025)
- [Neuromorphic Parameter Estimation for Power Converter Health Monitoring Using Spiking Neural Networks](https://mlsanity.com/paper/2604.15714/) (2026)

## Abstract (arXiv)

Spiking neural networks, also often referred to as the third generation of neural networks, carry the potential for a massive reduction in memory and energy consumption over traditional, second-generation neural networks. Inspired by the undisputed efficiency of the human brain, they introduce temporal and neuronal sparsity, which can be exploited by next-generation neuromorphic hardware. To open the pathway toward engineering applications, we introduce this exciting technology in the context of continuum mechanics. However, the nature of spiking neural networks poses a challenge for regression problems, which frequently arise in the modeling of engineering sciences. To overcome this problem, a framework for regression using spiking neural networks is proposed. In particular, a network topology for decoding binary spike trains to real numbers is introduced, utilizing the membrane potential of spiking neurons. As the aim of this contribution is a concise introduction to this new methodology, several different spiking neural architectures, ranging from simple spiking feed-forward to complex spiking long short-term memory neural networks, are derived. Several numerical experiments directed towards regression of linear and nonlinear, history-dependent material models are carried out. A direct comparison with counterparts of traditional neural networks shows that the proposed framework is much more efficient while retaining precision and generalizability. All code has been made publicly available in the interest of reproducibility and to promote continued enhancement in this new domain.