Compressible nozzle flows represent a challenge in aerospace engineering, requiring computational resources to resolve shock structures and turbulent transitions. This paper provides a review of Physics-Informed Machine Learning as a framework to address computational bottlenecks in Computational Fluid Dynamics (CFD). Principles of Physics-Informed Neural Networks are detailed, alongside methodological advances in loss engineering, dynamic weighting strategies, and the integration of artificial viscosity to stabilize shock wave resolution. The review examines hybrid and multi-fidelity architectures, such as DeepONet and extended PINNs, which enable flow prediction and geometry-aware generalization across irregular grids. Applications are analysed, including forward simulation of subsonic and supersonic branches, inverse estimation of fluid parameters, and the reconstruction of flow fields from sparse, noisy sensor data. Although PIML offers advantages in data efficiency and design acceleration, challenges remain in resolving discontinuities at high Reynolds numbers and ensuring training robustness. The conclusion identifies research opportunities in shock-aware learning, Bayesian uncertainty quantification, and scalable domain decomposition, offering a roadmap for the deployment of physics-informed tools in industrial nozzle design.
Keywords: PINNs, Physics-informed machine learning, compressible flow, hybrid CFD, inverse problems, nozzle flow, uncertainty quantification.
