Understanding Physics-Guided Machine Learning: Applications, Trends, and Challenges for Aerospace

The article provides a systematic review of the PGML concept as a new approach to modeling complex engineering problems in aerospace engineering. Particular attention is focused on how the integration of physical laws with machine learning algorithms transforms traditional approaches to analysis, design, and operation of structures. The principles underlying PGML are examined: modification of the loss function to account for residuals of physical equations, constructive embedding of symmetries into the model structure, and the development of a computational space based on physical invariants. The methodology of this work is based on the analysis of four aerospace-related problems: material fatigue prediction, flutter prediction—an aerodynamic phenomenon characterized by unstable self-oscillations of structures—design of thin-walled structures, and structural condition monitoring. Approximately 30 peer-reviewed sources were analyzed, enabling the identification of key directions for implementation in the design and analysis of the aerospace industry. A limitation of the PGML analysis is the limited number of published sources, which may be somewhat superficial. Key PGML implementations — namely PINNs, GAPINN, NSFnet, multi-fidelity, and hybrid models—and their effectiveness in cases of limited data samples are analyzed. Attention is also given to model interpretability issues, including the application of explainable ML, symbolic regression, and Bayesian approaches for solution verification in critical scenarios. The main challenges for widespread PGML adoption are identified: balancing physical and statistical components, scalability limitations in multiphase environments, certification complexity, and instability in solving inverse problems. The study concludes that PGML transcends being a mere application of machine learning and emerges as a new epistemological platform for formulating engineering hypotheses.