Physics-informed neural network: principles and applications

Abstract

This chapter delves into the fascinating characteristics of physics-informed neural networks (PINNs) by outlining their fundamental principles, including their mathematical foundations and structures. PINNs are designed by incorporating governing physical equations into the loss function as constraints, which helps to ensure precise output predictions even in areas with limited or no data. This chapter presents various strategies to apply PINNs to complex systems, thereby addressing the shortcomings of conventional PINNs. Additionally, multiphysics-informed neural networks (MPINNs) are introduced, with a special emphasis on complex mechatronic systems. The effectiveness of the MPINN framework is illustrated through examples such as an electric motor and a lithium-ion battery, demonstrating accurate and efficient multidimensional predictions for mechatronic systems despite limited data availability. These applications underscore the potential of MPINNs to mitigate data scarcity challenges in various industries.