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-model-based DNN framework, called Phy-Taylor, that accelerates learning
compliant representations with physical 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, we call {\em Physics-guided Neural Network Editing\}. The PhN aims
to directly capture nonlinearities inspired by physical quantities, such as
kinetic energy, potential energy, electrical power, and aerodynamic drag force.
To do so, the PhN augments neural network layers with two key components: (i)
monomials of Taylor series expansion of nonlinear functions capturing physical
knowledge, and (ii) a suppressor for mitigating the influence of noise. The
neural-network editing mechanism further modifies network links and activation
functions consistently with physical knowledge. As an extension, we also
propose a self-correcting Phy-Taylor framework that introduces two additional
capabilities: (i) physics-model-based safety relationship learning, and (ii)
automatic output correction when violations of safety occur. Through
experiments, we show that (by expressing hard-to-learn nonlinearities directly
and by constraining dependencies) Phy-Taylor features considerably fewer
parameters, and a remarkably accelerated training process, while offering
enhanced model robustness and accuracy.

该论文提出了一个基于物理模型的深度神经网络框架（Phy-Taylor），该框架主要包括物理兼容神经网络（PhN）和物理引导神经网络编辑机制。PhN 通过引入泰勒级数展开的单项式，捕获物理相关的非线性，Phy-Taylor 具有较少的参数，加快训练过程，提供了更好的模型鲁棒性和准确性。