From Ordinary Differential Equations to Structural Causal Models: the deterministic case

TL;DR

This paper explores how equilibrium states of first-order ODE systems can be represented using deterministic Structural Causal Models, clarifying causality concepts especially in cyclic models.

Contribution

It establishes conditions under which ODE equilibria can be modeled with SCMs, enhancing understanding of causality in dynamic systems.

Findings

Equilibrium states of ODEs can be described by SCMs under certain conditions.

Provides insights into causality in cyclic models within the SCM framework.

Clarifies the relationship between differential equations and causal modeling.

Abstract

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.