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

Abstract

Abstract. 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.