Hybrid Physics and Deep Learning Model for Interpretable Vehicle State Prediction

TL;DR

A hybrid approach combining deep learning and physical motion models including a novel two-phase training procedure is proposed, which can improve model interpretability with no decrease in accuracy compared to existing deep learning approaches.

Abstract

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.

Figures (5)

• Figure 1: The proposed hybrid architecture consists of physical model (regression and first-principles) and LSTM. Concatenation of vectors is represented by a black circle. The $+$-operators corresponds to an element-wise addition.
• Figure 2: Estimated ship state over $15min$. Lin-2P is the best performing model. True state is blue. Estimate is orange.
• Figure 3: Trajectory prediction is compared for baseline models and best hybrid model.
• Figure 4: Prediction error of Lin-2P for various thresholds is shown in orange. The performance of Lin-2P without constraints on the output is shown in blue. A performance comparable to the unconstrained model is achieved at a relative threshold of ${\sim}15\%$.
• Figure 5: Prediction error of MinQ+Qua-2P for various thresholds is shown in orange. The performance of MinQ+Qua-2P without constraints on the output is shown in blue. A performance comparable to the unconstrained model is achieved at a relative threshold of ${\sim} 8\%$.