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

Adrian Padilla-Segarra; Pascal Noble; Olivier Roustant; Éric Savin

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arXiv · 2507.17582

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

Adrian Padilla-Segarra·Pascal Noble·Olivier Roustant·Éric Savin

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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 present a general method for constraining a prescribed Gaussian process on an arbitrary compact set. The kernel of the pre-defined process must be at least continuous and may include other information about the studied phenomenon. This general boundary-constraining framework can be implemented with high flexibility for a broad range of engineering applications. From this, 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. We describe an adapted numerical method for the boundary-constraining procedure parameterized by a measure on the compact set. The relevance of the methodology 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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Adrian Padilla-Segarra, Pascal Noble, Olivier Roustant, Éric Savin. 2025-07-23. Physics-informed, boundary-constrained Gaussian process regression for the reconstruction of fluid flow fields. https://arxiv.org/abs/2507.17582

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