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.

C(NN)FD -- Deep Learning Modelling of Multi-Stage Axial Compressors Aerodynamics

The field of scientific machine learning and its applications to numerical analyses such as CFD has recently experienced a surge in interest. While its viability has been demonstrated in different domains, it has not yet reached a level of robustness and scalability to make it practical for industrial applications in the turbomachinery field. The highly complex, turbulent, and three-dimensional flows of multi-stage axial compressors for gas turbine applications represent a remarkably challenging case. This is due to the high-dimensionality of the regression of the flow-field from geometrical and operational variables, and the high computational cost associated with the large scale of the CFD domains. This paper demonstrates the development and application of a generalized deep learning framework for predictions of the flow field and aerodynamic performance of multi-stage axial compressors, also potentially applicable to any type of turbomachinery. A physics-based dimensionality reduction unlocks the potential for flow-field predictions for large-scale domains, re-formulating the regression problem from an unstructured to a structured one. The relevant physical equations are used to define a multi-dimensional physical loss function. Compared to "black-box" approaches, the proposed framework has the advantage of physically explainable predictions of overall performance, as the corresponding aerodynamic drivers can be identified on a 0D/1D/2D/3D level. An iterative architecture is employed, improving the accuracy of the predictions, as well as estimating the associated uncertainty. The model is trained on a series of dataset including manufacturing and build variations, different geometries, compressor designs and operating conditions. This demonstrates the capability to predict the flow-field and the overall performance in a generalizable manner, with accuracy comparable to the benchmark.

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.