mlsanityData to 7 Oct 2026

Learning the Hodgkin-Huxley Model with Operator Learning Techniques

arXiv 2406.02173 ↗First posted 4 Jun 2024math.NA cs.LG cs.NAcited by 10

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Abstract (arXiv)

We construct and compare three operator learning architectures, DeepONet, Fourier Neural Operator, and Wavelet Neural Operator, in order to learn the operator mapping a time-dependent applied current to the transmembrane potential of the Hodgkin- Huxley ionic model. The underlying non-linearity of the Hodgkin-Huxley dynamical system, the stiffness of its solutions, and the threshold dynamics depending on the intensity of the applied current, are some of the challenges to address when exploiting artificial neural networks to learn this class of complex operators. By properly designing these operator learning techniques, we demonstrate their ability to effectively address these challenges, achieving a relative L2 error as low as 1.4% in learning the solutions of the Hodgkin-Huxley ionic model.

Key facts. Cited by 10 papers in the map (data through 7 Oct 2026). Builds on 19 of its 54 references that are in the map. First posted on arXiv 4 Jun 2024.

Builds on

19 of 54 references.

References · 19

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7 more
  1. 2021Exponential Convergence of Deep Operator Networks for Elliptic Partial Differential Equationscited by 44
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Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2024: 2; 2025: 4; 2026: 4.

10 papers.

  1. 2025Learning High-dimensional Ionic Model Dynamics Using Fourier Neural Operatorscited by 2
  2. 2025NOBLE -- Neural Operator with Biologically-informed Latent Embeddings to Capture Experimental Variability in Biological Neuron Modelscited by 2
  3. 2025AMORE: Adaptive Multi-Output Operator Network for Stiff Chemical Kineticscited by 2
  4. 2024HyperSBINN: A Hypernetwork-Enhanced Systems Biology-Informed Neural Network for Efficient Drug Cardiosafety Assessmentcited by 1
  5. 2025Learning cardiac activation and repolarization times with operator learningcited by 1
  6. 2026Learning Hybrid Biophysical Neuron Models with Neural ODEscited by 1
  7. 2024A model learning framework for inferring the dynamics of transmission rate depending on exogenous variables for epidemic forecastscited by 0
  8. 2026Translation Invariance of Neural Operators for the FitzHugh-Nagumo Modelcited by 0
  9. 2026RTS Smoother-Guided Learning of Physics-Based Neural Differential Modelscited by 0
  10. 2026Retracing Hodgkin and Huxley: State Recovery Does Not Certify Mechanismcited by 0