Physics-Informed Neural Network for Solution of Nonlinear Differential Equations

In the recent years, machine learning techniques, notably deep learning, have emerged as vital tools in diverse arenas ranging from image recognition to agriculture, medicine, civil infrastructure, and even natural language processing. Of note, neural networks have been utilized in various engineering domains such as material science, fluid dynamics, and condition monitoring. Quite recently, a new category of neural networks, i.e. physics-informed neural networks (PINNs), has been introduced mainly to offer solution to linear and nonlinear differential equations. The core novelty of PINNs lies in their capacity to assimilate the underlying physical insights of a problem. Within the context of PINNs, the process of solving governing equations, encompassing both ordinary differential equations (ODEs) and partial differential equations (PDEs), involves the approximation of solutions through neural networks. The fine-tuning of these networks is achieved by optimizing a loss function, which factors in both the governing equation and its pertinent boundary and initial conditions. Impressively, PINNs have already demonstrated their prowess by accurately solving various ODEs and PDEs in diverse engineering contexts. In the ensuing chapter, we shall explore the utility of PINNs for solution of nonlinear differential equations in mechanical engineering.