From Deterministic ODEs to Dynamic Structural Causal Models

TL;DR

This paper explores the connection between Ordinary Differential Equations and Dynamic Structural Causal Models, showing how the asymptotic behavior of ODEs under interventions can be modeled dynamically, extending previous static equilibrium analyses.

Contribution

It introduces a novel framework linking ODEs to Dynamic Structural Causal Models, capturing dynamic intervention effects beyond static equilibrium analysis.

Findings

ODE asymptotic behavior can be modeled with Dynamic Structural Causal Models

Dynamic interventions are incorporated into causal modeling

Extends static equilibrium analysis to dynamic, time-varying interventions

Abstract

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.