← Back to all news
arXiv Machine Learning By Minjong Cheon

Low-Rank Kolmogorov-Arnold Generator Flows for Interpretable Operator Learning

Read the original on arXiv Machine Learning →

The paper introduces KAFlow, a low‑rank Kolmogorov‑Arnold flow that learns the generator of physical operators as a compact symbol composed of univariate Kolmogorov‑Arnold functions. By fixing the gauge of these functions, integrating dynamics with exact exponential integrators, and automatically distilling closed‑form expressions, KAFlow achieves markedly lower out‑of‑distribution loss and higher precision on synthetic benchmarks, long‑horizon quantum dynamics, and variable‑order fractional operators. The method recovers operator coefficients to within 10⁻⁴ and discovers complex dispersion relations that sparse regression cannot capture.

Machine-generated by The Flow from the publisher's headline and feed description — not written or checked by a human. The full article lives at arXiv Machine Learning.

Related stories

arXiv Machine Learning
Jul 27

Explainable quantum-compressed machine learning for complex fluid flows

arXiv:2607. 21688v1 Announce Type: cross Abstract: Machine-learning surrogates of physical systems face a paradox: explainable models facing the challenge of expressivity to capture complex nonlinear flows, whereas expressive deep surrogates match high-fidelity simulations only through massive parameterisations that turn the learned dynamics into a black box.

By Xiao Xue, Maida Wang, Mingyang Gao, Minh Chung, Peter V. Coveney
benchmarks
More like this →
arXiv Machine Learning
Jun 5

On the training of physics-informed neural operators for solving parametric partial differential equations

arXiv:2606. 06164v1 Announce Type: new Abstract: Physics-informed neural operators (PINOs) aim to learn solution operators for partial differential equations by using the governing physics as supervision, rather than relying solely on paired input-output simulation data.

By Nanxi Chen, Chuanjie Cui, Airong Chen, Sifan Wang, Rujin Ma
llmscomputer-visionbenchmarks
More like this →
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.

By Ramansh Sharma, Matthew Lowery, Houman Owhadi, Varun Shankar
benchmarks
More like this →