PO-CKAN: Physics-Informed Deep Operator Kolmogorov–Arnold Networks with Chunk-Rational Structure

Kolmogorov–Arnold Networks (KANs) offer superior expressivity over Multi-Layer Perceptrons (MLPs) but suffer from poor scalability due to the quadratic growth of parameters with network width. To address this bottleneck, we introduce PO-CKAN, a scalable physics-informed deep-operator framework built on Chunk-wise Rational Kolmogorov–Arnold Networks (CKANs). By embedding CKAN sub-networks within a DeepONet architecture, our framework combines parameter-efficient expressivity with a physics-informed residual loss that strictly enforces governing PDE constraints. This design ensures fast convergence and robust generalization across varying parameters, boundary conditions, and initial states. We validate PO-CKAN across Burgers', Eikonal, fractional, and diffusion–reaction benchmarks, where it consistently outperforms PI-DeepONet baselines. Notably, on the Burgers' equation with \nu=0.01, PO-CKAN achieves a 48% reduction in mean relative L^2 error compared to PI-DeepONet. These results establish PO-CKAN as a scalable, interpretable, and high-fidelity framework for physics-consistent operator learning.