A comprehensive review of theoretical concepts and advancements in physics-informed neural networks with applications in structural engineering
Surendra Baniya, Damodar Maity
Abstract
Abstract Structural engineering (SE) is a diverse field with numerous applications, including computational mechanics, structural simulation, and topology optimization, all governed by fundamental physical principles and typically addressed through classical numerical methods. These methods have delivered reliable and accurate solutions for forward problems within well-defined domains. However, they can become less effective when faced with high-dimensional spaces, complex geometries, irregular domains, or inverse problems with limited data. In parallel, data-driven models have gained popularity, but their dependence on large datasets and lack of physical interpretability restrict their generalization to unseen conditions. Physics-Informed Neural Networks (PINNs) have recently emerged as complementary tools that combine the strengths of numerical and data-driven approaches. By embedding governing physical laws directly into the learning process, PINNs reduce reliance on extensive datasets while improving interpretability and robustness. Although they may not yet rival classical solvers in terms of computational efficiency or accuracy for standard forward problems, PINNs offer unique advantages in scenarios where meshing is challenging, data and physics need to be integrated, or inverse problems require parameter identification and damage detection. This review provides a comprehensive overview of PINNs in SE, focusing on their theoretical framework, training strategies, computational implementations, and applications to both forward and inverse problems. The discussion highlights their advantages in accuracy, flexibility, and hybrid data-physics integration, while also outlining current limitations and future research directions to enhance their robustness and applicability for solving complex real-world SE problems.