Fine-tuning neural PDE operators to regime endpoints reveals a physical direction in weight space that CCM uses to compose accurate merged models for new or extrapolated regimes from metadata or short prefixes.
Fourier neural operator with learned deformations for pdes on general geometries.Journal of Machine Learning Research, 24(388):1–26
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UNVERDICTED 7representative citing papers
Local neural operators on 3x3x3 patches, composed via Schwarz iteration, solve large-scale nonlinear elasticity on arbitrary geometries without domain-specific retraining.
A finite element-guided physics-informed operator learning framework learns solution operators for coupled multiphysics PDEs, enabling discretization-independent predictions on arbitrary domains without labeled data.
FD-Bench supplies the first modular, reproducible benchmark and leaderboard for comparing neural PDE solvers on fluid dynamics tasks with direct numerical solver baselines.
U-HNO uses adaptive per-point routing in a U-shaped hybrid architecture to achieve state-of-the-art accuracy on PDE benchmarks with sharp localized features.
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.
DDS-PINN uses localized neural networks plus a unified global loss to model multiscale fluid flows with long-range dependencies, achieving CFD-comparable accuracy on laminar backward-facing step flow with zero data and O(10^-4) error on turbulent flow with only 500 supervision points.
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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.