Alexandra Baier

Multistep prediction models are essential for the simulation and model-predictive control of dynamical systems. Verifying the safety of such models is a multi-faceted problem requiring both systemtheoretic guarantees as well as establishing trust with human users. In this work, we propose a novel approach, ReLiNet (Recurrent Linear Parameter Varying Network), to ensure safety for multistep prediction of dynamical systems. Our approach simplifies a recurrent neural network to a switched linear system that is constrained to guarantee exponential stability, which acts as a surrogate for safety from a system-theoretic perspective. Furthermore, ReLiNet’s computation can be reduced to a single linear model for each time step, resulting in predictions that are explainable by definition, thereby establishing trust from a humancentric perspective. Our quantitative experiments show that ReLiNet achieves prediction accuracy comparable to that of state-of-the-art recurrent neural networks, while achieving more faithful and robust explanations compared to the model-agnostic explanation method of LIME.

Physical motion models offer interpretable predictions for the motion of vehicles. However, some model parameters, such as those related to aero- and hydrodynamics, are expensive to measure and are often only roughly approximated reducing prediction accuracy. Recurrent neural networks achieve high prediction accuracy at low cost, as they can use cheap measurements collected during routine operation of the vehicle, but their results are hard to interpret. To precisely predict vehicle states without expensive measurements of physical parameters, we propose a hybrid approach combining deep learning and physical motion models including a novel two-phase training procedure. We achieve interpretability by restricting the output range of the deep neural network as part of the hybrid model, which limits the uncertainty introduced by the neural network to a known quantity. We have evaluated our approach for the use case of ship and quadcopter motion. The results show that our hybrid model can improve model interpretability with no decrease in accuracy compared to existing deep learning approaches.