A supervised neural operator maps pixelated images of 2D domains to Dirichlet eigenvalues and eigenfunctions, achieving about 1% relative eigenvalue error on held-out random shapes.
A supervised neural network for drag prediction of arbitrary 2D shapes in low Reynolds number flows
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abstract
Despite the significant breakthrough of neural networks in the last few years, their spreading in the field of computational fluid dynamics is very recent, and many applications remain to explore. In this paper, we explore the drag prediction capabilities of convolutional neural networks for laminar, low-Reynolds number flows past arbitrary 2D shapes. A set of random shapes exhibiting a rich variety of geometrical features is built using B\'ezier curves. The efficient labelling of the shapes is provided using an immersed method to solve a unified Eulerian formulation of the Navier-Stokes equation. The network is then trained and optimized on the obtained dataset, and its predictive efficiency assessed on several real-life shapes, including NACA airfoils.
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2025 1verdicts
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Operator Inference for Elliptic Eigenvalue Problems
A supervised neural operator maps pixelated images of 2D domains to Dirichlet eigenvalues and eigenfunctions, achieving about 1% relative eigenvalue error on held-out random shapes.