Physics-Informed Deep Operator Network for Sparse-Sensor Reconstruction of Aerogel Insulator'S Overall Temperature Field Under Time-Varying Aerodynamic Heating Loads

Investigating the thermal insulation properties of SiO2 aerogels under large temperature differences is crucial for the development of thermal protection materials in hypersonic vehicles. Thus, a porous medium testing platform was established to evaluate aerogel insulation under constant heat flux, but diverse, time-varying aerodynamic loads in flight make experiments insufficient to capture global temperature fields. To address this challenge, a physics-informed deep operator network (PI-DeepONet) is proposed to accurately reconstruction the overall temperature field of aerogel under various heat flux conditions using sparse sensor data. This method reduces the temperature reconstruction error from approximately 10-2 (DeepONet) to around 10-3, with the maximum error remaining below 2%. From the reconstructed temperature fields, final surface temperatures at different positions along the thickness direction under varying temperature differences are extracted. The analysis reveals that aerogels with 79.55% porosity show superior insulation performance when the temperature difference exceeds 400 K. Furthermore, a comparison of the extrapolation performance of the two methods indicates that PI-DeepONet delivers higher prediction accuracy when facing operating conditions outside the training parameters. This method combines experimental measurements under constant heat flux with the extrapolation capabilities under time-varying heat loads, providing a reliable solution for temperature field reconstruction under aerodynamic heat loads.