Adaptive physics-informed neural network to simultaneously identify the temperature-dependent thermal conductivity and specific heat capacity of charring materials in hypersonic vehicle

The temperature-dependent thermal conductivity and specific heat capacity of charring materials are critical parameters in the design of thermal protection systems (TPS) for hypersonic vehicles. To enable simultaneous identification of these properties, we propose an adaptive physics-informed neural network (PINN) framework. This framework comprises four neural networks: three networks are employed to approximate the temperature, density, and mass flow rate fields, while a fourth network is dedicated to learning the temperature-dependent thermal conductivity and specific heat capacity. The networks are trained in parallel using a hybrid loss function that integrates physics-based constraints, data-driven residuals, and regularization terms. To effectively balance different measurement data, we introduce an adaptive weighting strategy. Numerical experiments demonstrate the superior performance of our framework. It significantly reduces the identification errors for thermal conductivity and specific heat capacity from 38.27 % and 43.94 % of a vanilla PINN to merely 2.55 % and 2.81 %, respectively. Notably, the identification errors remain 3.13 % and 6.28 % even with the measurement noise of 5 K. We also determine that a minimum of four temperature sensors is necessary for reliable identification. This study provides a powerful tool to accurately identify the thermal parameters in charring materials, facilitating modeling and optimization of TPS for hypersonic vehicles.