Differentiable Neural Operator for Temperature Field Prediction for Aerogel Thermal Insulation Materials at Large Temperature Differentials

Abstract To address the extreme aerodynamic heating challenges encountered by the leading edges of hypersonic vehicles, this study develops an aerogel-based thermal insulation material with engineering applicability. It proposes three deep neural operator models, Fourier Neural Operator, Deep Operator Network (DeepONet), and Transformer, for rapid prediction of the temperature field. These models establish an end-to-end mapping from multiple design parameters to the spatial temperature distribution. A global sensitivity analysis involving coupled design parameters is conducted to investigate the influence of different variables on thermal insulation performance. Results demonstrate that all three neural operator models achieve a maximum temperature prediction error of less than 5%, with prediction times reduced to the second level, representing a four-order-of-magnitude acceleration compared to conventional computational fluid dynamics methods. Furthermore, the Fourier Neural Operator model is employed as a surrogate to explore the impact of multiparameter design on thermal insulation performance. Sensitivity analysis indicates that thermal load and thermophysical properties (heat conduction phase and radiative attenuation) dominate the system response, contributing 87–91% of the total variance. The proposed neural operator framework offers a flexible and efficient alternative for predicting temperature fields in aerogel-based insulation systems, overcoming the limitations of traditional computational fluid dynamics methods in handling high-dimensional input spaces and providing valuable guidance for designing and optimizing advanced thermal insulation materials.