# P1-KAN: an effective Kolmogorov-Arnold network with application to hydraulic valley optimization

arXiv: https://arxiv.org/abs/2410.03801 · HTML: https://mlsanity.com/paper/2410.03801/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 41 references that are in the map.
- First posted on arXiv 4 Oct 2024.

## Builds on (most cited first, 23 of 23)

- [Gaussian Error Linear Units (GELUs)](https://mlsanity.com/paper/1606.08415/) (2016)
- [KAN: Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2404.19756/) (2024)
- [U-KAN Makes Strong Backbone for Medical Image Segmentation and Generation](https://mlsanity.com/paper/2406.02918/) (2024)
- [Kolmogorov-Arnold Networks are Radial Basis Function Networks](https://mlsanity.com/paper/2405.06721/) (2024)
- [Wav-KAN: Wavelet Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2405.12832/) (2024)
- [Chebyshev Polynomial-Based Kolmogorov-Arnold Networks: An Efficient Architecture for Nonlinear Function Approximation](https://mlsanity.com/paper/2405.07200/) (2024)
- [Kolmogorov-Arnold Networks (KANs) for Time Series Analysis](https://mlsanity.com/paper/2405.08790/) (2024)
- [DeepOKAN: Deep Operator Network Based on Kolmogorov Arnold Networks for Mechanics Problems](https://mlsanity.com/paper/2405.19143/) (2024)
- [Convolutional Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2406.13155/) (2024)
- [KAN or MLP: A Fairer Comparison](https://mlsanity.com/paper/2407.16674/) (2024)
- [Theoretical Issues in Deep Networks: Approximation, Optimization and Generalization](https://mlsanity.com/paper/1908.09375/) (2019)
- [TKAN: Temporal Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2405.07344/) (2024)
- [Kolmogorov-Arnold Networks for Time Series: Bridging Predictive Power and Interpretability](https://mlsanity.com/paper/2406.02496/) (2024)
- [Kolmogorov-Arnold Transformer](https://mlsanity.com/paper/2409.10594/) (2024)
- [BSRBF-KAN: A combination of B-splines and Radial Basis Functions in Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2406.11173/) (2024)
- [Demonstrating the Efficacy of Kolmogorov-Arnold Networks in Vision Tasks](https://mlsanity.com/paper/2406.14916/) (2024)
- [ReLU-KAN: New Kolmogorov-Arnold Networks that Only Need Matrix Addition, Dot Multiplication, and ReLU](https://mlsanity.com/paper/2406.02075/) (2024)
- [Neural networks-based algorithms for stochastic control and PDEs in finance](https://mlsanity.com/paper/2101.08068/) (2021)
- [Exploring the Limitations of Kolmogorov-Arnold Networks in Classification: Insights to Software Training and Hardware Implementation](https://mlsanity.com/paper/2407.17790/) (2024)
- [CoxKAN: Kolmogorov-Arnold Networks for Interpretable, High-Performance Survival Analysis](https://mlsanity.com/paper/2409.04290/) (2024)
- [Reduced Effectiveness of Kolmogorov-Arnold Networks on Functions with Noise](https://mlsanity.com/paper/2407.14882/) (2024)
- [Higher-order-ReLU-KANs (HRKANs) for solving physics-informed neural networks (PINNs) more accurately, robustly and faster](https://mlsanity.com/paper/2409.14248/) (2024)
- [Reservoir optimization and Machine Learning methods](https://mlsanity.com/paper/2106.08097/) (2021)

## Built on by (most cited first, 3 of 3)

- [Input Convex Kolmogorov Arnold Networks](https://mlsanity.com/paper/2505.21208/) (2025)
- [Learning operators on labelled conditional distributions with applications to mean field control of non exchangeable systems](https://mlsanity.com/paper/2603.21683/) (2026)
- [Hyper Input Convex Neural Networks for Shape Constrained Learning and Optimal Transport](https://mlsanity.com/paper/2604.26942/) (2026)

## Abstract (arXiv)

A new Kolmogorov-Arnold network (KAN) is proposed to approximate potentially irregular functions in high dimensions. We provide error bounds for this approximation, assuming that the Kolmogorov-Arnold expansion functions are sufficiently smooth. When the function is only continuous, we also provide universal approximation theorems. We show that it outperforms multilayer perceptrons in terms of accuracy and convergence speed. We also compare it with several proposed KAN networks: it outperforms all networks for irregular functions and achieves similar accuracy to the original spline-based KAN network for smooth functions. Finally, we compare some of the KAN networks in optimizing a French hydraulic valley.