Physics-informed, boundary-constrained Gaussian process regression for the reconstruction of fluid flow fields
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Abstract (arXiv)
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.
Key facts. Cited by 1 paper in the map (data through 14 Oct 2026). Builds on 15 of its 54 references that are in the map. First posted on arXiv 23 Jul 2025.
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References · 15
- 2020Fourier Neural Operator for Parametric Partial Differential Equationscited by 2,908
- 2019DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operatorscited by 2,018
- 2019Machine Learning for Fluid Mechanicscited by 385
- 2024Poseidon: Efficient Foundation Models for PDEscited by 200
- 2018Gaussian Processes and Kernel Methods: A Review on Connections and Equivalencescited by 192
- 2021Solving and Learning Nonlinear PDEs with Gaussian Processescited by 129
- 2022AirfRANS: High Fidelity Computational Fluid Dynamics Dataset for Approximating Reynolds-Averaged Navier-Stokes Solutionscited by 82
- 2018Kernel Flows: from learning kernels from data into the abysscited by 49
- 2022Information Theory with Kernel Methodscited by 37
- 2023Sparse Cholesky Factorization for Solving Nonlinear PDEs via Gaussian Processescited by 31
- 2020Gaussian Process Regression constrained by Boundary Value Problemscited by 15
- 2024Inferring turbulent velocity and temperature fields and their statistics from Lagrangian velocity measurements using physics-informed Kolmogorov-Arnold Networkscited by 15
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Citing papers per year: 2025: 1.
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