Physics-informed, boundary-constrained Gaussian process regression for the reconstruction of fluid flow fields

• URL: http://arxiv.org/abs/2507.17582v1
• Date: Wed, 23 Jul 2025 15:18:15 GMT
• Title: Physics-informed, boundary-constrained Gaussian process regression for the reconstruction of fluid flow fields
• Authors: Adrian Padilla-Segarra, Pascal Noble, Olivier Roustant, Éric Savin,
• Abstract summary: We derive physics-informed kernels for simulating two-dimensional velocity fields of an incompressible (divergence-free) flow around aerodynamic profiles.<n>These kernels allow to define Gaussian process priors satisfying the incompressibility condition and the prescribed boundary conditions along the profile in a continuous manner.
• Score: 1.2499537119440245
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Gaussian process regression techniques have been used in fluid mechanics for the reconstruction of flow fields from a reduction-of-dimension perspective. A main ingredient in this setting is the construction of adapted covariance functions, or kernels, to obtain such estimates. In this paper, we derive physics-informed kernels for simulating two-dimensional velocity fields of an incompressible (divergence-free) flow around aerodynamic profiles. These kernels allow to define Gaussian process priors satisfying the incompressibility condition and the prescribed boundary conditions along the profile in a continuous manner. Such physical and boundary constraints can be applied to any pre-defined scalar kernel in the proposed methodology, which is very general and can be implemented with high flexibility for a broad range of engineering applications. Its relevance and performances are illustrated by numerical simulations of flows around a cylinder and a NACA 0412 airfoil profile, for which no observation at the boundary is needed at all.

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