From Deterministic ODEs to Dynamic Structural Causal Models
This provides a novel perspective for researchers in causal modeling, linking ODEs and SCMs, but it appears incremental as it builds on earlier work by focusing on dynamic interventions.
The paper tackles the relationship between Ordinary Differential Equations (ODEs) and Structural Causal Models (SCMs), showing that under certain conditions, the asymptotic behavior of ODEs under non-constant interventions can be modeled using Dynamic SCMs, extending beyond static equilibria to dynamic asymptotic behavior.
Structural Causal Models are widely used in causal modelling, but how they relate to other modelling tools is poorly understood. In this paper we provide a novel perspective on the relationship between Ordinary Differential Equations and Structural Causal Models. We show how, under certain conditions, the asymptotic behaviour of an Ordinary Differential Equation under non-constant interventions can be modelled using Dynamic Structural Causal Models. In contrast to earlier work, we study not only the effect of interventions on equilibrium states; rather, we model asymptotic behaviour that is dynamic under interventions that vary in time, and include as a special case the study of static equilibria.