Local neural operators on 3x3x3 patches, composed via Schwarz iteration, solve large-scale nonlinear elasticity on arbitrary geometries without domain-specific retraining.
Fourier neural operator with learned deformations for pdes on general geometries.Journal of Machine Learning Research, 24(388):1–26
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FluidFlow uses conditional flow-matching with U-Net and DiT architectures to predict pressure and friction coefficients on airfoils and 3D aircraft meshes, outperforming MLP baselines with better generalization.
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Neural-Schwarz Tiling for Geometry-Universal PDE Solving at Scale
Local neural operators on 3x3x3 patches, composed via Schwarz iteration, solve large-scale nonlinear elasticity on arbitrary geometries without domain-specific retraining.
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FluidFlow: a flow-matching generative model for fluid dynamics surrogates on unstructured meshes
FluidFlow uses conditional flow-matching with U-Net and DiT architectures to predict pressure and friction coefficients on airfoils and 3D aircraft meshes, outperforming MLP baselines with better generalization.