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| Main Authors: | , |
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| Format: | Preprint |
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2025
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| Online Access: | https://arxiv.org/abs/2510.08795 |
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| _version_ | 1866911247292694528 |
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| author | Wu, Junyi Lin, Guang |
| author_facet | Wu, Junyi Lin, Guang |
| contents | 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 $ν=0.01$, 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_08795 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | PO-CKAN:Physics Informed Deep Operator Kolmogorov Arnold Networks with Chunk Rational Structure Wu, Junyi Lin, Guang Machine Learning Mathematical Physics 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 $ν=0.01$, 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. |
| title | PO-CKAN:Physics Informed Deep Operator Kolmogorov Arnold Networks with Chunk Rational Structure |
| topic | Machine Learning Mathematical Physics |
| url | https://arxiv.org/abs/2510.08795 |