Neural Operator-Enabled Aerodynamic Load Estimation for Hypersonics

This work expands on a strain-based aerodynamic sensing strategy for hypersonics to account for nonlinear temperature effects in real time. The sensing strategy uses sparse strain observations to infer the aerodynamic pressure loads, which is mathematically posed as a partial differential equation (PDE)-constrained inverse problem. In previous work, this inverse problem was shown to have a closed-form solution, where offline computation of the operations requiring the PDE solution was exploited to enable real-time evaluation speeds. In this work, the temperature effects preclude the offline pre-computation acceleration because the PDE operator is nonlinearly temperature dependent. To address this challenge, the recently developed neural matrix operator (NEMO) approach is employed to account for the temperature dependence. The NEMO method explicitly incorporates the physics structure of the governing equations, and thus preserves the availability of a closed-form inverse solution that can be computed rapidly onboard the vehicle. This work further considers the tasks of estimating the temperature field from sparse temperature measurements, and compensation for the thermal strain. The overall performance is demonstrated on the Initial Concept 3.X hypersonic vehicle. The results show strong approximation performance of NEMO and corresponding inverse solution accuracy, but further work is necessary to reduce errors in the thermal strain compensation.