mlsanityData to 7 Oct 2026

SMS: Spiking Marching Scheme for Efficient Long Time Integration of Differential Equations

arXiv 2211.09928 ↗First posted 17 Nov 2022math.NA cs.LG cs.NAcited by 5

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Abstract (arXiv)

We propose a Spiking Neural Network (SNN)-based explicit numerical scheme for long time integration of time-dependent Ordinary and Partial Differential Equations (ODEs, PDEs). The core element of the method is a SNN, trained to use spike-encoded information about the solution at previous timesteps to predict spike-encoded information at the next timestep. After the network has been trained, it operates as an explicit numerical scheme that can be used to compute the solution at future timesteps, given a spike-encoded initial condition. A decoder is used to transform the evolved spiking-encoded solution back to function values. We present results from numerical experiments of using the proposed method for ODEs and PDEs of varying complexity.

Key facts. Cited by 5 papers in the map (data through 7 Oct 2026). Builds on 16 of its 44 references that are in the map. First posted on arXiv 17 Nov 2022.

Builds on

16 of 44 references.

References · 16

  1. 2019DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operatorscited by 1,965
  2. 2019Class-Balanced Loss Based on Effective Number of Samplescited by 1,239
  3. 2019Surrogate Gradient Learning in Spiking Neural Networkscited by 604
  4. 2020Going Deeper With Directly-Trained Larger Spiking Neural Networkscited by 268
  5. 2018Deep Learning in Spiking Neural Networkscited by 258
  6. 2021Training Spiking Neural Networks Using Lessons From Deep Learningcited by 251
  7. 2016Training Deep Spiking Neural Networks using Backpropagationcited by 203
  8. 2020Enabling Deep Spiking Neural Networks with Hybrid Conversion and Spike Timing Dependent Backpropagationcited by 142
  9. 2021Optimal Conversion of Conventional Artificial Neural Networks to Spiking Neural Networkscited by 134
  10. 2019PPINN: Parareal Physics-Informed Neural Network for time-dependent PDEscited by 116
  11. 2021Efficient Neuromorphic Signal Processing with Loihi 2cited by 90
  12. 2021Long-time integration of parametric evolution equations with physics-informed DeepONetscited by 87
4 more
  1. 2022Learning two-phase microstructure evolution using neural operators and autoencoder architecturescited by 72
  2. 2021Beyond Classification: Directly Training Spiking Neural Networks for Semantic Segmentationcited by 54
  3. 2016Conversion of Artificial Recurrent Neural Networks to Spiking Neural Networks for Low-power Neuromorphic Hardwarecited by 39
  4. 2022Spiking Neural Operators for Scientific Machine Learningcited by 8

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2023: 3; 2024: 0; 2025: 1; 2026: 1.

5 papers.

  1. 2025Operator Learning for Reconstructing Flow Fields from Sparse Measurements: an Energy Transformer Approachcited by 11
  2. 2023Understanding and Mitigating Extrapolation Failures in Physics-Informed Neural Networkscited by 8
  3. 2023Neuroscience inspired scientific machine learning (Part-1): Variable spiking neuron for regressioncited by 5
  4. 2023Neuroscience inspired scientific machine learning (Part-2): Variable spiking wavelet neural operatorcited by 1
  5. 2026Operator Learning for Reconstructing Flow Fields from Sparse Measurements: a Language Model Approachcited by 0