Phy-Taylor: Physics-Model-Based Deep Neural Networks

TL;DR

Phy-Taylor introduces a physics-informed neural network framework that accelerates training, reduces parameters, and ensures physical compliance, improving robustness and accuracy in modeling physical systems.

Contribution

It proposes a novel physics-model-based neural network architecture with a compliance mechanism and self-correcting capabilities, advancing physical consistency in deep learning models.

Findings

Fewer parameters needed for accurate modeling.

Accelerated training process observed.

Enhanced robustness and physical compliance.

Abstract

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.