Modeling and simulation techniques are today extensively used both in industry and science. Parts of larger systems are, however, typically modeled and simulated by different techniques, tools, and algorithms. In addition, experts from different disciplines use various modeling and simulation techniques. Both these facts make it difficult to study coupled heterogeneous systems. Co-simulation is an emerging enabling technique, where global simulation of a coupled system can be achieved by composing the simulations of its parts. Due to its potential and interdisciplinary nature, co-simulation is being studied in different disciplines but with limited sharing of findings. In this survey, we study and survey the state-of-the-art techniques for co-simulation, with the goal of enhancing future research and highlighting the main challenges. To study this broad topic, we start by focusing on discrete-event-based co-simulation, followed by continuous-time-based co-simulation. Finally, we explore the interactions between these two paradigms, in hybrid co-simulation. To survey the current techniques, tools, and research challenges, we systematically classify recently published research literature on co-simulation, and summarize it into a taxonomy. As a result, we identify the need for finding generic approaches for modular, stable, and accurate coupling of simulation units, as well as expressing the adaptations required to ensure that the coupling is correct.

Dynamical systems see widespread use in natural sciences like physics, biology, and chemistry, as well as engineering disciplines such as circuit analysis, computational fluid dynamics, and control. For simple systems, the differential equations governing the dynamics can be derived by applying fundamental physical laws. However, for more complex systems, this approach becomes exceedingly difficult. Data-driven modeling is an alternative paradigm that seeks to learn an approximation of the dynamics of a system using observations of the true system. In recent years, there has been an increased interest in applying data-driven modeling techniques to solve a wide range of problems in physics and engineering. This article provides a survey of the different ways to construct models of dynamical systems using neural networks. In addition to the basic overview, we review the related literature and outline the most significant challenges from numerical simulations that this modeling paradigm must overcome. Based on the reviewed literature and identified challenges, we provide a discussion on promising research areas.