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

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.

Deep learning modelling of tip clearance variations on multi-stage axial compressors aerodynamics

Application of deep learning methods to physical simulations such as CFD (Computational Fluid Dynamics) for turbomachinery applications, have been so far of limited industrial relevance. This paper demonstrates the development and application of a deep learning framework for real-time predictions of the impact of tip clearance variations on the flow field and aerodynamic performance of multi-stage axial compressors in gas turbines. The proposed architecture is proven to be scalable to industrial applications, and achieves in real-time accuracy comparable to the CFD benchmark. The deployed model, is readily integrated within the manufacturing and build process of gas turbines, thus providing the opportunity to analytically assess the impact on performance and potentially reduce requirements for expensive physical tests.

C(NN)FD -- a deep learning framework for turbomachinery CFD analysis

Deep Learning methods have seen a wide range of successful applications across different industries. Up until now, applications to physical simulations such as CFD (Computational Fluid Dynamics), have been limited to simple test-cases of minor industrial relevance. This paper demonstrates the development of a novel deep learning framework for real-time predictions of the impact of manufacturing and build variations on the overall performance of axial compressors in gas turbines, with a focus on tip clearance variations. The associated scatter in efficiency can significantly increase the $CO_2$ emissions, thus being of great industrial and environmental relevance. The proposed \textit{C(NN)FD} architecture achieves in real-time accuracy comparable to the CFD benchmark. Predicting the flow field and using it to calculate the corresponding overall performance renders the methodology generalisable, while filtering only relevant parts of the CFD solution makes the methodology scalable to industrial applications.