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

• URL: http://arxiv.org/abs/2510.08795v2
• Date: Mon, 03 Nov 2025 16:54:38 GMT
• Title: PO-CKAN:Physics Informed Deep Operator Kolmogorov Arnold Networks with Chunk Rational Structure
• Abstract summary: PO-CKAN is a physics-informed deep operator framework based on Chunkwise Rational Kolmogorov-Arnold-Arnold Networks (KANs)
• Score: 10.56081138054608
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We propose PO-CKAN, a physics-informed deep operator framework based on Chunkwise Rational Kolmogorov--Arnold Networks (KANs), for approximating the solution operators of partial differential equations. This framework leverages a Deep Operator Network (DeepONet) architecture that incorporates Chunkwise Rational Kolmogorov-Arnold Network (CKAN) sub-networks for enhanced function approximation. The principles of Physics-Informed Neural Networks (PINNs) are integrated into the operator learning framework to enforce physical consistency. This design enables the efficient learning of physically consistent spatio-temporal solution operators and allows for rapid prediction for parametric time-dependent PDEs with varying inputs (e.g., parameters, initial/boundary conditions) after training. Validated on challenging benchmark problems, PO-CKAN demonstrates accurate operator learning with results closely matching high-fidelity solutions. PO-CKAN adopts a DeepONet-style branch--trunk architecture with its sub-networks instantiated as rational KAN modules, and enforces physical consistency via a PDE residual (PINN-style) loss. On Burgers' equation with $\nu=0.01$, PO-CKAN reduces the mean relative $L^2$ error by approximately 48\% compared to PI-DeepONet, and achieves competitive accuracy on the Eikonal and diffusion--reaction benchmarks.

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