From Ordinary Differential Equations to Structural Causal Models: the deterministic case
This work addresses a theoretical problem for researchers in causality and dynamical systems, providing incremental insights into the relationship between ODEs and SCMs.
The paper tackles the problem of linking Ordinary Differential Equation (ODE) systems to deterministic Structural Causal Models (SCMs), showing conditions under which equilibrium states of ODEs can be described by SCMs, with a focus on clarifying causality in cyclic models.
We show how, and under which conditions, the equilibrium states of a first-order Ordinary Differential Equation (ODE) system can be described with a deterministic Structural Causal Model (SCM). Our exposition sheds more light on the concept of causality as expressed within the framework of Structural Causal Models, especially for cyclic models.