Deep operator learning-based surrogate models for aerothermodynamic analysis of AEDC hypersonic waverider

Abstract: Neural networks are universal approximators that traditionally have been used to learn a map between function inputs and outputs. However, recent research has demonstrated that deep neural networks can be used to approximate operators, learning function-to-function mappings. Creating surrogate models to supplement computationally expensive hypersonic aerothermodynamic models in characterizing the response of flow fields at different angles of attack (AoA) is an ideal application of neural operators. We investigate the use of neural operators to infer flow fields (volume and surface quantities) around a geometry based on a 3D waverider model based on experimental data measured at the Arnold Engineering Development Center (AEDC) Hypervelocity Wind Tunnel Number 9. We use a DeepONet neural operator which consists of two neural networks, commonly called a branch and a trunk network. The final output is the inner product of the output of the branch network and the output of the trunk net. Because the flow field contains shocks across the entire volume, we conduct a two-step training approach of the DeepONet that facilitates accurate approximation of solutions even in the presence of discontinuities. We train various DeepONet models to understand and predict pressure $(p)$, density $(\rho)$, velocity $(u)$, heat flux $(Q_w)$, and total shear stress $(\tau_{w})$ for the AEDC waverider geometry at Ma=7.36 across AoA that range from $-10^{\circ}$ to $10^{\circ}$ for surface quantities and from $-14^{\circ}$ to $14^{\circ}$ for volume quantities.