Statistical Design of Thermal Protection System Using Physics-Informed Neural Network

Thermal protection systems of space vehicles are designed computationally rather than experimentally. They are validated using ground experiments, but all aspects of the flight cannot be replicated on ground. This ground-to-flight mapping introduces uncertainties which need to be accounted for while designing any thermal protection system. Thus, precise computational models along with uncertainty quantification in the models are required to design the TPS. The focus of this study is to estimate the thermal material parameters of TPS based on the target reliability requirements using statistical methods. To perform uncertainty quantification of a system, a simulated model of the system needs to be solved many times on statistical samples, increasing the computational time and cost of the overall process. In this study, a physics-informed neural network model is used in the analysis instead of traditional physics-based numerical solutions. The accuracy of PINN is comparable to that of the numerical solution. To find the parameter distribution, sampling of the parameter space is performed using Sequential Monte-Carlo method. The sampling method is efficient as it generates samples based on the target distribution in parallel. The framework can approximate the parameter distributions that satisfy the TPS design reliability constraints. The framework achieved a remarkable increase in the speed; specifically, the time required to process 10,000 samples was reduced 175 times using the proposed PINN-SMC. This reliability analysis can be used for design optimization of the TPS based on risk analysis along with other systems of the vehicle.