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Data-driven shape inference in three-dimensional steady-state supersonic flows: Optimizing a discrete loss with JAX-Fluids

Aaron B. Buhendwa1,*, Deniz A. Bezgin1,†, Petr Karnakov2,‡, Nikolaus A. Adams1,3,§, and Petros Koumoutsakos2,∥

  • 1Technical University of Munich, School of Engineering and Design, Chair of Aerodynamics and Fluid Mechanics, Boltzmannstraße 15, 85748 Garching bei München, Germany
  • 2Computational Science and Engineering Laboratory, Harvard University, Cambridge, Massachusetts 02138, USA
  • 3Technical University of Munich, Munich Institute of Integrated Materials, Energy and Process Engineering, Lichtenbergstraße 4a, 85748 Garching bei München, Germany

  • *Contact author: aaron.buhendwa@tum.de
  • †Contact author: deniz.bezgin@tum.de
  • ‡Contact author: pkarnakov@gmail.com
  • §Contact author: nikolaus.adams@tum.de
  • ∥Contact author: petros@seas.harvard.edu
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Phys. Rev. Fluids 10, 084902 – Published 12 August, 2025

DOI: https://doi.org/10.1103/9wj9-nmr8

Abstract

We present a data- and first-principles-driven method for inferring the shape of a solid obstacle and its flow field in three-dimensional steady-state supersonic flows. The proposed method combines the optimizing a discrete loss (ODIL) technique with the automatically differentiable JAX-Fluids computational fluid dynamics (CFD) solver to study the joint reconstruction of flow fields and obstacle shapes. ODIL minimizes the discrete residual of the governing partial differential equation (PDE) by gradient descent-based algorithms. The ODIL framework inherits the characteristics of the chosen numerical discretization of the underlying PDE, including its consistency and stability. Discrete residuals and their automatic differentiation gradients are computed by the JAX-Fluids solver, which provides nonlinear shock-capturing schemes and level-set-based immersed solid boundaries. We use synthetic data to validate this approach on challenging inverse problems, including the shape inference of a solid obstacle in three-dimensional steady-state supersonic flow. Specifically, we study flows around a cylinder, a sphere, and an ellipse. We investigate two distinct approaches for the obstacle shape representation: (1) parametric shape representation, where the obstacle is described by a small set of parameters (e.g., the radius of the cylinder and the sphere) that are optimized together with the flow field, and (2) free shape representation, where the level-set function is directly optimized at each point of the computational mesh, without relying on predefined shapes. For the former, a thorough comparison with physics-informed neural networks is provided. We show that the nonlinear shock-capturing discretization in combination with the level-set-based interface representation allows for accurate inference of the obstacle shape and its flow field for the ODIL method. The proposed approach opens new avenues for solving complex inverse problems in supersonic aerodynamics.

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Phys. Rev. Fluids 10, 084902– Published 12 August, 2025
  • Received 26 August 2024
  • Accepted 16 June 2025
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