Beyond Particle Systems: Operator Networks

Particle systems are used for simulating non-linear dynamics of complex systems. They are computationally attractive, because the models are simple difference equations. The difference equations, however, constitute a closed system lacking scalability and intentionality; it is hard to "reverse engineer" the equations, to understand the relations of the variables and coefficients to the dynamics displayed by the simulation. Consequently, much of the modeling work goes into finding workarounds. In this paper, we study a potential solution. As the main contribution, we formalize particle system computations as mathematical operator networks, to gain intentionality and modularity. Operators also support the inclusion of processes outside the mathematical domain of difference equations. We illustrate the use of operator networks by simulating the construction and dynamics of an hourglass.