Data-driven shape inference in three-dimensional steady state supersonic flows using ODIL and JAX-Fluids

TL;DR

This paper introduces a novel data- and physics-based method combining ODIL and JAX-Fluids to accurately infer 3D obstacle shapes and flow fields in steady-state supersonic flows, validated on synthetic data.

Contribution

It develops a joint shape and flow inference framework using ODIL with differentiable CFD, enabling accurate 3D shape reconstruction in supersonic aerodynamics.

Findings

Accurate shape inference for cylinders, spheres, and ellipses in 3D flows.

Effective joint reconstruction of flow fields and obstacle shapes.

Comparison showing advantages over Physics-Informed Neural Networks.

Abstract

We present a novel 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 method combines the Optimizing a Discrete Loss (ODIL) technique with the automatically differentiable JAX-Fluids CFD solver to jointly reconstruct flow fields and obstacle shapes. ODIL minimizes the discrete residual of the governing PDE via gradient descent-based algorithms and inherits the consistency and stability of the chosen numerical discretization. Discrete residuals and their gradients are computed using JAX-Fluids, which features nonlinear shock-capturing schemes and level-set-based immersed solid boundaries. We validate our method on synthetic data for challenging inverse problems, including shape inference of solid obstacles in 3D steady-state supersonic flows. In particular, we study flow around a cylinder, sphere, and ellipse. Two shape representations are investigated: (1) parametric, where the shape is described by a small set of parameters (e.g., radius of the cylinder or sphere) optimized jointly with the flow field, and (2) free-form, where the level-set function is optimized pointwise over the mesh without predefined shapes. For the parametric case, we provide a detailed comparison with Physics-Informed Neural Networks. We demonstrate that the combination of nonlinear shock-capturing discretization and level-set-based interface representation enables accurate inference of obstacle shapes and flow fields via the ODIL method. This approach opens new avenues for solving complex inverse problems in supersonic aerodynamics.