# Learning Hybrid Biophysical Neuron Models with Neural ODEs

arXiv: https://arxiv.org/abs/2606.16693 · HTML: https://mlsanity.com/paper/2606.16693/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 41 references that are in the map.
- First posted on arXiv 15 Jun 2026.

## Builds on (most cited first, 17 of 17)

- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Efficiently Modeling Long Sequences with Structured State Spaces](https://mlsanity.com/paper/2111.00396/) (2021)
- [Augmented Neural ODEs](https://mlsanity.com/paper/1904.01681/) (2019)
- [Universal Differential Equations for Scientific Machine Learning](https://mlsanity.com/paper/2001.04385/) (2020)
- [On Neural Differential Equations](https://mlsanity.com/paper/2202.02435/) (2022)
- [Equinox: neural networks in JAX via callable PyTrees and filtered transformations](https://mlsanity.com/paper/2111.00254/) (2021)
- [Stiff Neural Ordinary Differential Equations](https://mlsanity.com/paper/2103.15341/) (2021)
- [Bayesian Neural Ordinary Differential Equations](https://mlsanity.com/paper/2012.07244/) (2020)
- [Learning the Hodgkin-Huxley Model with Operator Learning Techniques](https://mlsanity.com/paper/2406.02173/) (2024)
- [Learning Physics Informed Neural ODEs With Partial Measurements](https://mlsanity.com/paper/2412.08681/) (2024)
- [Identifiability Challenges in Sparse Linear Ordinary Differential Equations](https://mlsanity.com/paper/2506.09816/) (2025)
- [Uncertainty and Structure in Neural Ordinary Differential Equations](https://mlsanity.com/paper/2305.13290/) (2023)
- [Comparing Physics-Informed and Neural ODE Approaches for Modeling Nonlinear Biological Systems: A Case Study Based on the Morris-Lecar Model](https://mlsanity.com/paper/2603.26921/) (2026)
- [Towards an Hybrid Hodgkin-Huxley Action Potential Generation Model](https://mlsanity.com/paper/2304.01346/) (2023)
- [Physics-Informed Neural ODEs with Scale-Aware Residuals for Learning Stiff Biophysical Dynamics](https://mlsanity.com/paper/2511.11734/) (2025)
- [An Empirical Investigation of Neural ODEs and Symbolic Regression for Dynamical Systems](https://mlsanity.com/paper/2601.20637/) (2026)

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

- [Retracing Hodgkin and Huxley: State Recovery Does Not Certify Mechanism](https://mlsanity.com/paper/2609.34566/) (2026)

## Abstract (arXiv)

Biophysical neuron models link measurements of neural activity to underlying cellular mechanisms. Yet, a central challenge is that the kinetics of many ion channels are poorly characterized, and practical simplifications -- omitting channels or reducing morphological detail -- introduce systematic gaps between model and biology. Bridging these gaps requires approaches that can flexibly discover unmodeled dynamics while preserving mechanistic interpretability. Here, we introduce a hybrid modeling framework that embeds neural ordinary differential equations into conductance-based biophysical models to capture unknown currents or mis-specified channel kinetics. By parameterizing the neural ODE in terms of voltage-dependent steady-state and time-constant functions, we recover interpretable gating dynamics directly from voltage recordings without assuming a functional form. We show that the hybrid model fits the gating kinetics of 2400 ion channel models and recovers unknown gating dynamics from single current-clamp recordings, generalizing to out-of-distribution stimulus regimes under realistic inputs and parameter misspecification. We also use our method to reduce a multicompartment model of a cortical neuron into a single-compartment hybrid model with a learned axial current, yielding up to an order of magnitude lower computational cost. Together, our results establish a plug-and-play framework for selectively replacing unknown components of conductance-based models with neural ODEs while preserving their mechanistic structure.