A comprehensive analysis of PINNs: Variants, Applications, and Challenges

TL;DR

This survey provides a comprehensive overview of Physics Informed Neural Networks (PINNs), covering their architecture, variants, applications, challenges, and future research directions to facilitate broader adoption.

Contribution

It offers the first detailed, integrated analysis of PINNs architecture, variants, performance, challenges, and future directions, filling gaps left by previous superficial surveys.

Findings

PINNs show promising results across various differential equations.

Performance varies significantly with architecture and application domain.

Key challenges include standardization and scalability.

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.