Learning Hypersonic Flow Fields from Sparse Data Using Multi-Fidelity Deep Operator Networks

Hypersonic flow simulations are essential for optimizing lift, drag, and shape in aircraft design but remain computationally intensive due to nonlinear compressible Navier–Stokes equations and air-dissociation chemistry, which demand tiny time steps and fine grids. Generating high-fidelity data is both costly and sparse. We develop a neural-operator surrogate that delivers rapid, accurate, and generalizable predictions of hypersonic flow fields over a conical body across varying Mach numbers and altitudes. A DeepONet learns mappings from one infinite dimensional function space (Mach number, altitude) to another infinite dimensional function space (flow fields) without full PDE discretization. We further introduce a novel multi-fidelity DeepONet architecture that fuses low and high-fidelity data via a combined loss function. High-fidelity samples were produced with NASA FUN3D (≈6 k core-hours) and low-fidelity with CBAero (7 s/sample). After 10 k epochs, the single-fidelity DeepONet trained in 43.3 s (0.338 s inference) with 8.12 % L₂ error; the multi-fidelity variant trained in 79.2 s (0.747 s inference) with 6.60 % error. Multi-fidelity neural operators thus offer a scalable, data-efficient approach to hypersonic flow modeling, slashing simulation costs and accelerating aerodynamic design.