Phy-Taylor: Partially Physics-Knowledge-Enhanced Deep Neural Networks via NN Editing

Purely data-driven deep neural networks (DNNs) applied to physical engineering systems can infer relations that violate physics laws, thus leading to unexpected consequences. To address this challenge, we propose a physics-knowledge-enhanced DNN framework called Phy-Taylor, accelerating learning-compliant representations with physics knowledge. The Phy-Taylor framework makes two key contributions; it introduces a new architectural physics-compatible neural network (PhN) and features a novel compliance mechanism, which we call physics-guided neural network (NN) editing. The PhN aims to directly capture nonlinear physical quantities, such as kinetic energy, electrical power, and aerodynamic drag force. To do so, the PhN augments NN layers with two key components: 1) monomials of the Taylor series for capturing physical quantities and 2) a suppressor for mitigating the influence of noise. The NN editing mechanism further modifies network links and activation functions consistently with physics knowledge. As an extension, we also propose a self-correcting Phy-Taylor framework for safety-critical control of autonomous systems, which introduces two additional capabilities: 1) safety relationship learning and 2) automatic output correction when safety violations occur. Through experiments, we show that Phy-Taylor features considerably fewer parameters and a remarkably accelerated training process while offering enhanced model robustness and accuracy.