A Hybrid Physics-Augmented Neural Network for Dynamic System Modeling with Partially Known Dynamics

This paper introduces Hybrid Physics-Augmented Neural Network (HyPA-Net), a hybrid modeling framework that integrates physics-based linear time-invariant models with artificial neural networks (ANNs) to address dynamic system modeling when only partial physical knowledge is available. The approach leverages the interpretability and robustness of established physical models while using ANNs—such as long short-term memory architectures—to capture unknown or nonlinear system behaviors. The methodology normalizes state and input variables for compatibility with ANN training and expands traditional recursive state-space equations for efficient backpropagation over sequences. Vehicle dynamics, specifically using a rear-wheel steering test case, validate the proposed framework. Various HyPA-Net configurations are benchmarked against pure physics-based and pure data-driven models, demonstrating improved prediction accuracy and model flexibility. The experimental results in this application confirm that hybrid models yield superior performance over strict physical approaches and can implicitly approximate submodel dynamics within a unified, yet modular, architecture, opening avenues for applications in domains where partial physics-based knowledge is available but insufficient on its own.