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Towards a universal formalism for modeling & simulation

The representation of hybrid systems has shown to be one of the greatest challenges in Modeling & simulation. While discrete event systems can be represented without error, continuous models rely on approximations based in numerical methods. Given the large variety of numerical integrators a unified representation has been elusive due the lack of an universal formalism that can describe all numerical methods and to provide their seamless integration. In this paper, we propose the Hybrid Flow System Specification (HYFLOW) as a unifying representation for different families of numerical integrators for solving ordinary differential equations (ODEs). HYFLOW combines the conventional discrete event approach with a novel representation based on sampling and the support for dense outputs to describe modular and hierarchical hybrid systems. We demonstrate that HYFLOW can describe 1st-order, geometric (2nd-order), and exponential integrators. Additionally, since these integrators share the same underlaying HYFLOW representation they can be seamlessly combined.