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

arXiv: https://arxiv.org/abs/2510.08795 · HTML: https://mlsanity.com/paper/2510.08795/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 51 references that are in the map.
- First posted on arXiv 9 Oct 2025.

## Builds on (most cited first, 21 of 21)

- [DeepSDF: Learning Continuous Signed Distance Functions for Shape Representation](https://mlsanity.com/paper/1901.05103/) (2019)
- [Sigmoid-Weighted Linear Units for Neural Network Function Approximation in Reinforcement Learning](https://mlsanity.com/paper/1702.03118/) (2017)
- [DGM: A deep learning algorithm for solving partial differential equations](https://mlsanity.com/paper/1708.07469/) (2017)
- [Solving high-dimensional partial differential equations using deep learning](https://mlsanity.com/paper/1707.02568/) (2017)
- [Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets](https://mlsanity.com/paper/2103.10974/) (2021)
- [B-PINNs: Bayesian Physics-Informed Neural Networks for Forward and Inverse PDE Problems with Noisy Data](https://mlsanity.com/paper/2003.06097/) (2020)
- [Physics-Constrained Deep Learning for High-dimensional Surrogate Modeling and Uncertainty Quantification without Labeled Data](https://mlsanity.com/paper/1901.06314/) (2019)
- [Wav-KAN: Wavelet Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2405.12832/) (2024)
- [KAN 2.0: Kolmogorov-Arnold Networks Meet Science](https://mlsanity.com/paper/2408.10205/) (2024)
- [Kolmogorov-Arnold Networks (KANs) for Time Series Analysis](https://mlsanity.com/paper/2405.08790/) (2024)
- [A survey on modern trainable activation functions](https://mlsanity.com/paper/2005.00817/) (2020)
- [DeepOKAN: Deep Operator Network Based on Kolmogorov Arnold Networks for Mechanics Problems](https://mlsanity.com/paper/2405.19143/) (2024)
- [KAN or MLP: A Fairer Comparison](https://mlsanity.com/paper/2407.16674/) (2024)
- [Pad'e Activation Units: End-to-end Learning of Flexible Activation Functions in Deep Networks](https://mlsanity.com/paper/1907.06732/) (2019)
- [Kolmogorov-Arnold Network for Satellite Image Classification in Remote Sensing](https://mlsanity.com/paper/2406.00600/) (2024)
- [Neural networks and rational functions](https://mlsanity.com/paper/1706.03301/) (2017)
- [Predictive Modeling of Flexible EHD Pumps using Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2405.07488/) (2024)
- [Smooth Kolmogorov Arnold networks enabling structural knowledge representation](https://mlsanity.com/paper/2405.11318/) (2024)
- [iKAN: Global Incremental Learning with KAN for Human Activity Recognition Across Heterogeneous Datasets](https://mlsanity.com/paper/2406.01646/) (2024)
- [Initial Investigation of Kolmogorov-Arnold Networks (KANs) as Feature Extractors for IMU Based Human Activity Recognition](https://mlsanity.com/paper/2406.11914/) (2024)
- [Operator Learning Enhanced Physics-informed Neural Networks for Solving Partial Differential Equations Characterized by Sharp Solutions](https://mlsanity.com/paper/2310.19590/) (2023)

## Built on by (most cited first, 1 of 1)

- [Learning Unsteady Aneurysm Hemodynamics with Physics-Informed DeepONets](https://mlsanity.com/paper/2608.13629/) (2026)

## Abstract (arXiv)

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 L2 error by approximately 48% compared to PI-DeepONet, and achieves competitive accuracy on the Eikonal and diffusion--reaction benchmarks.