Physics-Informed Neural Networks for Solving Physical Partial Differential Equations in Aerospace Engineering

This analytical study aims to synthesize recent advances in Physics-Informed Neural Networks (PINNs) and assess their applicability for solving physical partial differential equations in aerospace engineering. The analysis integrates findings from benchmark problems such as flow over a cylinder, the NACA0012 airfoil, and the inverse Burgers’ equation, highlighting methodological developments including gradient-enhanced and volume-weighted formulations, adaptive sampling, transfer learning, and geometry-aware or isogeometric extensions. The results demonstrate that volume-weighted PINNs achieve 1–3% accuracy compared with reference CFD solutions and reduce viscosity estimation errors to approximately 1.5% in inverse problems. These findings confirm the theoretical potential of PINNs to unify physical modeling, data assimilation, and inverse analysis within a consistent computational framework. At the same time, practical deployment remains limited by the representational capacity of standard architectures in high-compressibility and multiscale regimes. Addressing these challenges requires the use of multi-frequency and weak-form neural formulations, as well as verifiable error estimates and generalization metrics for realistic geometries. Thus, the study provides both a systematization of the state of the art and a roadmap for developing physics-grounded, data-efficient modeling techniques in future aerodynamic design and simulation.<p></p>