Featured Application: Performing effective and efficient hybrid simulations of mechanical systems in real-time by implementing a model order reduction technique to the computational algorithm. The efficiency of the computations is understood as the ability to test systems of a higher number of degrees of freedom while maintaining high accuracy, without increasing the time step. Effective simulation is a simulation that allows acquiring correct results while maintaining the time regime.Abstract: Hybrid simulation is a technique for testing mechanical systems. It applies to structures with elements hard or impossible to model numerically. These elements are tested experimentally by straining them by means of actuators, while the rest of the system is simulated numerically using a finite element method (FEM). Data is interchanged between experiment and simulation. The simulation is performed in real-time in order to accurately recreate the dynamic behavior in the experiment. FEM is very computationally demanding, and for systems with a great number of degrees of freedom (DOFs), real-time simulation with small-time steps (ensuring high accuracy) may require powerful computing hardware or may even be impossible. The author proposed to swap the finite element (FE) model with an artificial neural network (ANN) to significantly lower the computational cost of the real-time algorithm. The presented examples proved that the computational cost could be reduced by at least one number of magnitude while maintaining high accuracy of the simulation; however, obtaining appropriate ANN was not trivial and might require many attempts. subsystem, which are measured in the form of a vector r P i+1 , where subsequent elements of the vector correspond to degrees of freedom (DOFs) of the discretized FE model [4,5]. Appl. Sci. 2019, 9, x FOR PEER REVIEW 2 of 19 are measured in the form of a vector r P i+1, where subsequent elements of the vector correspond to degrees of freedom (DOFs) of the discretized FE model [4,5].