Hugging Face Trending Papers
Neural Operator Splitting for Fluid Dynamics in Complex Geometry
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arXiv Machine Learning
Oct 21
Neural Operator Splitting for Fluid Dynamics in Complex Geometry
arXiv:2610.27671v1 Announce Type: new Abstract: Solving dynamical systems in complex and diverse geometries remains challenging for both numerical solvers and learning-based surrogate models. We prop...
arXiv Machine Learning
Oct 8
Fluids You Can Trust: Property-Preserving Operator Learning for Incompressible Flows
The paper introduces a kernel‑based operator learning method that preserves key physical properties—such as incompressibility, periodicity, and turbulence—of the incompressible Navier–Stokes equations. By mapping input functions to expansion coefficients in a property‑preserving kernel basis, the method guarantees that predicted velocity fields analytically maintain these properties. The authors provide theoretical convergence guarantees, develop efficient computational techniques for large‑scale training, and demonstrate significant accuracy and speed improvements over neural operators on 2D and 3D flow benchmarks.
arXiv Machine Learning
Jun 16
ANCHOR: Error-Controlled Adaptive Numerical Correction for Neural Operator Time Marching
arXiv:2512. 19643v2 Announce Type: replace Abstract: Numerical simulation of time-dependent partial differential equations (PDEs) is central to scientific and engineering applications, but high-fidelity solvers are often prohibitively expensive for long-horizon or time-critical settings.
arXiv Machine Learning
Sep 22
Discretization-independent operator learning for partial differential equations
arXiv:2507.07292v2 Announce Type: replace Abstract: We develop a new and general encode-approximate-reconstruct operator learning model that leverages learned neural representations of bases for inpu...
arXiv Machine Learning
Jun 11
Hybrid Iterative Neural Low-Regularity Integrator for Nonlinear Dispersive Equations
arXiv:2605. 04853v2 Announce Type: replace Abstract: We propose HIN-LRI, a hybrid framework that augments a classical numerical solver with a neural operator trained to correct the solver's structured truncation error.
arXiv Machine Learning
Jul 16
Leveraging Differentiable PDE Solvers for Semi-Neural Spatial Reconstruction From Sparse Measurements
arXiv:2601. 20496v2 Announce Type: replace-cross Abstract: Generating dense physical fields from sparse measurements is a fundamental question in sampling, signal processing, and many other applications.