# Neural Ordinary Differential Equations for Intervention Modeling

arXiv: https://arxiv.org/abs/2010.08304 · HTML: https://mlsanity.com/paper/2010.08304/

## Key facts

- Cited by 19 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 Oct 2020.

## Built on by (most cited first, 19 of 19)

- [Continuous-Time Modeling of Counterfactual Outcomes Using Neural Controlled Differential Equations](https://mlsanity.com/paper/2206.08311/) (2022)
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- [CF-GODE: Continuous-Time Causal Inference for Multi-Agent Dynamical Systems](https://mlsanity.com/paper/2306.11216/) (2023)
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- [ODE Discovery for Longitudinal Heterogeneous Treatment Effects Inference](https://mlsanity.com/paper/2403.10766/) (2024)
- [Causal Graph ODE: Continuous Treatment Effect Modeling in Multi-agent Dynamical Systems](https://mlsanity.com/paper/2403.00178/) (2024)
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- [A statistical approach to latent dynamic modeling with differential equations](https://mlsanity.com/paper/2311.16286/) (2023)
- [Exploring Neural Ordinary Differential Equations as Interpretable Healthcare classifiers](https://mlsanity.com/paper/2503.03129/) (2025)
- [Analysis of ODE2VAE with Examples](https://mlsanity.com/paper/2108.04899/) (2021)
- [Neural State-Space Modeling with Latent Causal-Effect Disentanglement](https://mlsanity.com/paper/2209.12387/) (2022)
- [Continuous time recurrent neural networks: overview and application to forecasting blood glucose in the intensive care unit](https://mlsanity.com/paper/2304.07025/) (2023)
- [Symmetry-regularized neural ordinary differential equations](https://mlsanity.com/paper/2311.16628/) (2023)
- [Breaking Free: Decoupling Forced Systems with Laplace Neural Networks](https://mlsanity.com/paper/2503.13158/) (2025)
- [Automatic and Structure-Aware Sparsification of Hybrid Neural ODEs](https://mlsanity.com/paper/2505.18996/) (2025)

## Abstract (arXiv)

By interpreting the forward dynamics of the latent representation of neural networks as an ordinary differential equation, Neural Ordinary Differential Equation (Neural ODE) emerged as an effective framework for modeling a system dynamics in the continuous time domain. However, real-world systems often involves external interventions that cause changes in the system dynamics such as a moving ball coming in contact with another ball, or such as a patient being administered with particular drug. Neural ODE and a number of its recent variants, however, are not suitable for modeling such interventions as they do not properly model the observations and the interventions separately. In this paper, we propose a novel neural ODE-based approach (IMODE) that properly model the effect of external interventions by employing two ODE functions to separately handle the observations and the interventions. Using both synthetic and real-world time-series datasets involving interventions, our experimental results consistently demonstrate the superiority of IMODE compared to existing approaches.