Predictive modeling of flexible EHD pumps using Kolmogorov-Arnold Networks

Abstract

We present a novel approach to predicting the pressure and flow rate of flexible electrohydrodynamic pumps using the Kolmogorov-Arnold Network. Inspired by the Kolmogorov-Arnold representation theorem, KAN replaces fixed activation functions with learnable spline-based activation functions, enabling it to approximate complex nonlinear functions more effectively than traditional models like Multi-Layer Perceptron and Random Forest. We evaluated KAN on a dataset of flexible EHD pump parameters and compared its performance against RF, and MLP models. KAN achieved superior predictive accuracy, with Mean Squared Errors of 12.186 and 0.012 for pressure and flow rate predictions, respectively. The symbolic formulas extracted from KAN provided insights into the nonlinear relationships between input parameters and pump performance. These findings demonstrate that KAN offers exceptional accuracy and interpretability, making it a promising alternative for predictive modeling in electrohydrodynamic pumping.

Keywords

Kolmogorov-Arnold Networks / Electrohydrodynamic pumps / Neural network

CRediT authorship contribution statement

Yanhong Peng: Writing - original draft, Validation, Project administration, Methodology, Funding acquisition, Conceptualization. Yuxin Wang: Project administration, Investigation, Conceptualization. Fangchao Hu: Validation. Miao He: Validation, Methodology. Zebing Mao: Conceptualization, Data curation, Methodology, Resources. Xia Huang: Supervision, Project administration. Jun Ding: Supervision, Project administration.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgments

This paper was supported by Innovative Research Group of Chongqing Municipal Education Commission (CXQT19026), and Cooperative Project between Chinese Academy of Sciences and University in Chongqing (HZ2021011). Moreover, this work was supported by the Research Startup Fund of Chongqing University of Technology (0119240197).

References

[1] Y. Peng, D. Li, X. Yang, Z. Ma, Z. Mao, A review on electrohydrodynamic (EHD) pump, Micromachines 14 (2) (2023) 321.

[2] Z. Mao, X. Bai, Y. Peng, Y. Shen, Design, modeling, and characteristics of ring-shaped robot actuated by functional fluid, 2024, arXiv preprint arXiv:2406.08135.

[3] M. Enayati, M.-W. Chang, F. Bragman, M. Edirisinghe, E. Stride, Electrohy-drodynamic preparation of particles, capsules and bubbles for biomedical engineering applications, Colloids Surf. A 382 (1-3) (2011) 154-164.

[4] Z. Mao, Y. Peng, C. Hu, R. Ding, Y. Yamada, S. Maeda, Soft computing-based predictive modeling of flexible electrohydrodynamic pumps, Biomimetic Intell. Robotics 3 (3) (2023) 100114.

[5] Z. Liu, Y. Wang, S. Vaidya, F. Ruehle, J. Halverson, M. Soljačić, T.Y. Hou, M. Tegmark, KAN: Kolmogorov-arnold networks, 2024, arXiv preprint arXiv: 2404.19756.

[6] D.C. Liu, J. Nocedal, On the limited memory BFGS method for large scale optimization, Math. Program. 45 (1) (1989) 503-528.

[7] C. Zhang, J. Chen, J. Li, Y. Peng, Z. Mao, ‘Large language models for human-robot interaction: A review, Biomimetic Intell. Robotics (2023) 100131.