Physics-Guided Machine Learning via Feature-Level Augmentation in an LSTM Model for Temperature Prediction in High-Speed Missile Radomes

For high-speed missiles, aerodynamic heating introduces significant thermal challenges that must be addressed early in the design phase. Accurate temperature prediction is critical, yet traditional methods—like wind tunnel tests or numerical simulations—are often too time-consuming for rapid design cycles. Even fast engineering solvers become bottlenecks during large-scale studies such as Design of Experiments, where thousands of flight conditions must be evaluated. Recent advances in machine learning, enable neural networks to deliver near-instantaneous predictions across large datasets, reducing computation time from hours to seconds. Furthermore, their millisecond-level response times per case make them ideal for real-time or onboard applications, where rapid thermal assessment is essential for guidance, decision-making and protection. In this study, a Physics-Guided Machine Learning (PGML) framework is adopted to predict transient along-surface and through-thickness temperature distributions in high-speed missile radomes. A multi-layer Long Short-Term Memory (LSTM) neural network is trained using data generated from a previously validated physics-based solver benchmarked against CFD and experimental data in the literature. The model incorporates an analytical stagnation temperature relation, which serves as a physics-informed feature to guide the model in both training and testing. This hybridization of data-driven learning with minimal physics injection significantly improves the model’s ability to capture sharp thermal transients and reduces limitations of purely black-box models. The proposed LSTM model delivers fast and reliable predictions, capturing sharp thermal transients with a maximum discrepancy of \(1.71\%\), supporting next-generation thermal design workflows.