A comprehensive analysis of PINNs: Variants, Applications, and Challenges
Afila Ajithkumar Sophiya, Akarsh K Nair, Sepehr Maleki, Senthil K. Krishnababu
TL;DR
This survey provides a comprehensive synthesis of Physics Informed Neural Networks (PINNs), detailing their core architecture (neural surrogate, automatic differentiation, physics-informed loss), and surveying variants (cPINN, XPINN, APINN, fPINN, BiPDE) and extensions (grid-free, fractional PDEs). It covers solving ODEs, PDEs, and fractional differential equations, and highlights real-world applications in medicine, power systems, and fluid mechanics, along with challenges such as convergence, computational cost, and theory. The work identifies key contributions, including architecture analyses, performance insights across equation classes, and forward-looking directions for optimization, generalization, and theoretical guarantees. The practical impact lies in guiding researchers toward standardized methodologies, robust variants, and scalable applications in physics-informed learning.
Abstract
Physics Informed Neural Networks (PINNs) have been emerging as a powerful computational tool for solving differential equations. However, the applicability of these models is still in its initial stages and requires more standardization to gain wider popularity. Through this survey, we present a comprehensive overview of PINNs approaches exploring various aspects related to their architecture, variants, areas of application, real-world use cases, challenges, and so on. Even though existing surveys can be identified, they fail to provide a comprehensive view as they primarily focus on either different application scenarios or limit their study to a superficial level. This survey attempts to bridge the gap in the existing literature by presenting a detailed analysis of all these factors combined with recent advancements and state-of-the-art research in PINNs. Additionally, we discuss prevalent challenges in PINNs implementation and present some of the future research directions as well. The overall contributions of the survey can be summarised into three sections: A detailed overview of PINNs architecture and variants, a performance analysis of PINNs on different equations and application domains highlighting their features. Finally, we present a detailed discussion of current issues and future research directions.