DTE AICCOMAS 2025

Neural Operator-Based Modeling of Hypersonic Flows Around Varying Geometries

  • Peyvan, Ahmad (Brown University)
  • Karniadakis, George (Brown University)

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Neural operator networks (DeepONet) constitute a class of neural network models designed to acquire the mapping between input and output spaces. These operators have two significant attributes: they can generalize across various spatial resolutions and can approximate nonlinear operators effectively. These features make them particularly suitable for learning solutions to the nonlinear Navier-Stokes equations, which govern hypersonic flows over varying geometries. Simulating such flows with traditional flows entails substantial computational costs, as it necessitates accounting for thermodynamic, chemical kinetic, and transport phenomena, including mass diffusion, viscosity, and heat conductivity, particularly in thermally and chemically non-equilibrium conditions. Therefore, deep learning surrogate models can be used to accelerate the prediction such complicated flows. A notable challenge in hypersonic flow modeling is predicting the formation of strong shock waves in front of the flying object. Recent advancements in numerical schemes capable of robustly resolving hypersonic flows have enabled simulations at Mach 10 around a semi-elliptical geometry. This research seeks to develop a deep learning model that translates the geometry of a semi-ellipse—characterized by varying lengths of semi-minor and semi-major axes—into flow field variables such as density, pressure, and velocity components. Given that Vanilla DeepONet struggles to accurately capture discontinuous solutions, Peyvan et al. [2] introduced an interpretable neural operator framework called RiemannONet, which successfully learns extremely strong shock waves. We have adapted the RiemannONet framework to facilitate the mapping from geometry to flow field. This deep learning model can later be utilized for shape optimization purposes.