A generalizable supervised operator learning framework based on Kolmogorov–Arnold networks for structured grid generation with boundary control

Abstract

Mesh quality is paramount for the accuracy of numerical simulations. Structured grids are favored in engineering for their superior discretization, yet their generation faces an inherent trade-off between quality and efficiency. Physics-informed neural network approaches rapidly generate high-quality meshes, yet they are constrained by limited generalizability, requiring retraining for varying geometry inputs. In this paper, we propose a model termed MKoNet, a generalizable supervised operator learning framework for structured grid generation with boundary control. The model utilizes operator learning to directly capture the underlying physical laws governing the partial differential equations (PDEs), thereby generating high-quality meshes for varying geometric boundaries without the need for retraining. Specifically, our loss function incorporates a dedicated boundary-control term, which alleviates the severe element distortion near boundaries observed in existing methods and improves mesh quality. Furthermore, we replace traditional multi-layer perceptrons (MLPs) with Kolmogorov–Arnold networks (KANs), achieving enhanced model performance with a substantially reduced parameter count. Experimental results across diverse geometric configurations demonstrate that MKoNet can generate high-quality structured grids with effective boundary control and strong robustness. The proposed method achieves competitive or superior performance across most evaluated metrics, particularly for challenging geometries with complex boundaries.

The authors' abstract, as published at the source. Engineering Applications of Artificial Intelligence, 2026 · DOI ↗