# Hybrid2 Neural ODE Causal Modeling and an Application to Glycemic Response

arXiv: https://arxiv.org/abs/2402.17233 · HTML: https://mlsanity.com/paper/2402.17233/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- Builds on 39 of its 83 references that are in the map.
- First posted on arXiv 27 Feb 2024.

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

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [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)
- [Empirical Evaluation of Gated Recurrent Neural Networks on Sequence Modeling](https://mlsanity.com/paper/1412.3555/) (2014)
- [Autoformer: Decomposition Transformers with Auto-Correlation for Long-Term Series Forecasting](https://mlsanity.com/paper/2106.13008/) (2021)
- [An Empirical Evaluation of Generic Convolutional and Recurrent Networks for Sequence Modeling](https://mlsanity.com/paper/1803.01271/) (2018)
- [Learning to Simulate Complex Physics with Graph Networks](https://mlsanity.com/paper/2002.09405/) (2020)
- [Learning Mesh-Based Simulation with Graph Networks](https://mlsanity.com/paper/2010.03409/) (2020)
- [On the Parameterization and Initialization of Diagonal State Space Models](https://mlsanity.com/paper/2206.11893/) (2022)
- [Universal Differential Equations for Scientific Machine Learning](https://mlsanity.com/paper/2001.04385/) (2020)
- [Stable Architectures for Deep Neural Networks](https://mlsanity.com/paper/1705.03341/) (2017)
- [On Neural Differential Equations](https://mlsanity.com/paper/2202.02435/) (2022)
- [Graph networks as learnable physics engines for inference and control](https://mlsanity.com/paper/1806.01242/) (2018)
- [Techniques for Interpretable Machine Learning](https://mlsanity.com/paper/1808.00033/) (2018)
- [Temporal Convolutional Networks: A Unified Approach to Action Segmentation](https://mlsanity.com/paper/1608.08242/) (2016)
- [Integrating Scientific Knowledge with Machine Learning for Engineering and Environmental Systems](https://mlsanity.com/paper/2003.04919/) (2020)
- [Graph Neural Ordinary Differential Equations](https://mlsanity.com/paper/1911.07532/) (2019)
- [The Causal-Neural Connection: Expressiveness, Learnability, and Inference](https://mlsanity.com/paper/2107.00793/) (2021)
- [Augmenting Physical Models with Deep Networks for Complex Dynamics Forecasting](https://mlsanity.com/paper/2010.04456/) (2020)
- [Multivariate Time Series Forecasting with Dynamic Graph Neural ODEs](https://mlsanity.com/paper/2202.08408/) (2022)
- [Physics-Integrated Variational Autoencoders for Robust and Interpretable Generative Modeling](https://mlsanity.com/paper/2102.13156/) (2021)
- [Hybrid Forecasting of Chaotic Processes: Using Machine Learning in Conjunction with a Knowledge-Based Model](https://mlsanity.com/paper/1803.04779/) (2018)
- [Neural Causal Models for Counterfactual Identification and Estimation](https://mlsanity.com/paper/2210.00035/) (2022)
- [Integrating Expert ODEs into Neural ODEs: Pharmacology and Disease Progression](https://mlsanity.com/paper/2106.02875/) (2021)
- [Combining data assimilation and machine learning to infer unresolved scale parametrisation](https://mlsanity.com/paper/2009.04318/) (2020)
- [A Framework for Machine Learning of Model Error in Dynamical Systems](https://mlsanity.com/paper/2107.06658/) (2021)
- [Learning Dynamical Systems from Partial Observations](https://mlsanity.com/paper/1902.11136/) (2019)
- [Graph Neural Networks Accelerated Molecular Dynamics](https://mlsanity.com/paper/2112.03383/) (2021)
- [Auto-differentiable Ensemble Kalman Filters](https://mlsanity.com/paper/2107.07687/) (2021)
- [ChemNODE: A Neural Ordinary Differential Equations Approach for Chemical Kinetics Solvers](https://mlsanity.com/paper/2101.04749/) (2020)

## Built on by (most cited first, 13 of 13)

- [Position: Biology is the Challenge Physics-Informed ML Needs to Evolve](https://mlsanity.com/paper/2510.25368/) (2025)
- [SPIN-ODE: Stiff Physics-Informed Neural ODE for Chemical Reaction Rate Estimation](https://mlsanity.com/paper/2505.05625/) (2025)
- [The Driver-Blindness Phenomenon: Why Deep Sequence Models Default to Autocorrelation in Blood Glucose Forecasting](https://mlsanity.com/paper/2511.20601/) (2025)
- [Structural Constraints for Physics-augmented Learning](https://mlsanity.com/paper/2410.05507/) (2024)
- [Sharpness-Aware Hybrid Model Learning for Architecture-Agnostic Parameter Estimation](https://mlsanity.com/paper/2602.06837/) (2026)
- [MCMC Informed Neural Emulators for Uncertainty Quantification in Dynamical Systems](https://mlsanity.com/paper/2603.10987/) (2026)
- [Bayesian Nonparametric Mixed-Effect ODEs with Gaussian Processes](https://mlsanity.com/paper/2605.13088/) (2026)
- [PhysioSeq2Seq: A Hybrid Physiological Digital Twin and Sequence-to-Sequence LSTM for Long-Horizon Glucose Forecasting in Type 1 Diabetes](https://mlsanity.com/paper/2605.16860/) (2026)
- [OrthoReg: Orthogonal Regularization for Hybrid Symbolic-Neural Dynamical Systems](https://mlsanity.com/paper/2606.19145/) (2026)
- [Interventional Flow Matching: Prospective Dose-Response Forecasting with Velocity-Field Jacobian Regularization](https://mlsanity.com/paper/2606.29386/) (2026)
- [Quantum-Inspired Vision: Leveraging Wave-Particle Duality for Low-Illumination Enhancement](https://mlsanity.com/paper/2607.01731/) (2026)
- [Causal Retention in Interactive Agents: Interface Factorization and Selective Adaptation](https://mlsanity.com/paper/2609.30650/) (2026)
- [On the Divergence of Accuracy and Mechanism Consistency in Time Series World Models](https://mlsanity.com/paper/2610.01842/) (2026)

## Abstract (arXiv)

Hybrid models composing mechanistic ODE-based dynamics with flexible and expressive neural network components have grown rapidly in popularity, especially in scientific domains where such ODE-based modeling offers important interpretability and validated causal grounding (e.g., for counterfactual reasoning). The incorporation of mechanistic models also provides inductive bias in standard blackbox modeling approaches, critical when learning from small datasets or partially observed, complex systems. Unfortunately, as the hybrid models become more flexible, the causal grounding provided by the mechanistic model can quickly be lost. We address this problem by leveraging another common source of domain knowledge: ranking of treatment effects for a set of interventions, even if the precise treatment effect is unknown. We encode this information in a causal loss that we combine with the standard predictive loss to arrive at a hybrid loss that biases our learning towards causally valid hybrid models. We demonstrate our ability to achieve a win-win, state-of-the-art predictive performance and causal validity, in the challenging task of modeling glucose dynamics post-exercise in individuals with type 1 diabetes.