Real‐time models for systems with costly or unknown dynamics

Many applications require real‐time simulation where the computer model can be executed at least as fast as the underlying physical system. However, as the complexity of models grows, for example, in case of flexible multibody dynamics accounting for body elasticity, this becomes harder even with high‐end computers and parallel computing. Further the modeling itself could be too cumbersome to come up with causal models, especially in industrial applications, or modeling is inhibited by unknown physical effects. In such cases, data‐based modeling with AI‐strategies may be an alternative to come up with real‐time capable simulation models. Based on measured or costly simulated trajectories, state function values of the dynamic system are first identified from divided differences of subsequent states, and then used for training a feedforward neural network. This can then be used as an approximate surrogate for further simulations or as part of a real‐time application. Applications to the Duffing equation and a closed‐loop mechanism demonstrate high conformity of predicted and directly simulated trajectories reproducing even the bifurcation behavior of the Duffing equation.