Hybrid$^2$ Neural ODE Causal Modeling and an Application to Glycemic Response

TL;DR

This paper introduces a hybrid neural ODE model that combines mechanistic and neural components, incorporating causal knowledge through a novel causal loss to improve predictive accuracy and causal validity in modeling glucose dynamics.

Contribution

It proposes a new hybrid loss function that maintains causal grounding in neural ODE models, enhancing interpretability and performance in complex scientific systems.

Findings

Achieved state-of-the-art predictive accuracy in glucose modeling.

Maintained causal validity through the proposed causal loss.

Demonstrated effectiveness in small and partially observed datasets.

Abstract

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: \emph{ranking} of treatment effects for a set of interventions, even if the precise treatment effect is unknown. We encode this information in a \emph{causal loss} that we combine with the standard predictive loss to arrive at a \emph{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 \emph{and} causal validity, in the challenging task of modeling glucose dynamics post-exercise in individuals with type 1 diabetes.