Causal.jl:\A Modeling and Simulation Framework for Causal Models

This paper introduces a modeling and simulation framework, Causal.jl, that enables fast and effective system simulations and online and offline data analyzes. Causal.jl adopts a causal modeling approach in which a model consists of components that process data and the connections that transfer the data flowing between these components. The framework developed makes it possible to simulate discrete time or continuous time, static or dynamical systems. In particular, it is possible to simulate dynamical systems modeled by various types of equations such as the ordinary, random ordinary, stochastic, delayed differential, differentialalgebraic equations, and discrete-time difference equations. During the simulation, the data flowing through the connections can be processed online and offline, and specialized analyzes can be performed. These analyzes can also be enriched with plugins that can be easily defined using the standard Julia library or various Julia packages. The simulation is performed by evolving the model components between sampling time intervals individually and in parallel. The independent evolution of the components allows the simulation of the models consisting of the components represented by different mathematical equations, while the parallel evolution of components increases the simulation performance.