[Paper Review] Predictive Modeling of Flexible EHD Pumps using Kolmogorov-Arnold Networks

Yanhong Peng, Wang, Yuxin+5 more|arXiv (Cornell University)|May 13, 2024

Hydraulic and Pneumatic Systems5 citations

TL;DR

The paper introduces Kolmogorov-Arnold Networks (KAN) to predict pressure and flow rate of flexible EHD pumps, outperforming RF and MLP and providing interpretable symbolic formulas.

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 0.001 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.

Motivation & Objective

• Motivate accurate prediction of pressure and flow rate in flexible electrohydrodynamic pumps.
• Develop a KAN-based model leveraging learnable spline activation to capture nonlinear input-output relationships.
• Compare KAN with RF and MLP in predictive performance on a flexible EHD pump dataset.
• Provide interpretable symbolic formulas that reveal relationships between input features and pump performance.

Proposed method

• Represent f(x) via Kolmogorov-Arnold layer architecture with learnable spline activations on edges.
• Construct two KAN models for pressure and flow rate with specified widths and spline orders (pressure: width=[5,2,1], k=3; flow rate: width=[5,6,1], k=4).
• Train using small-dataset optimization (LBFGS) with sparsity regularization, followed by pruning and retraining.
• Extract symbolic formulas by approximating learned splines with mathematical expressions.
• Compare KAN against Random Forest and MLP on 90-10 train-test split (88 train, 10 test) using MSE as the metric.

Experimental results

Research questions

• RQ1 Can KAN provide higher predictive accuracy for pressure and flow rate of flexible EHD pumps than RF and MLP?
• RQ2 Do learnable spline activations in KAN improve modeling nonlinear input-output relationships for EHD pump performance?
• RQ3 Can symbolic formulas extracted from KAN yield interpretable insights into parameter influences on pressure and flow rate?

Key findings

Model	Pressure MSE	Flow Rate MSE
KAN	12.186	0.012
Random Forest	1750.017	0.040
MLP	78.329	0.002

• KAN achieves superior predictive accuracy for both outputs (pressure MSE = 12.186; flow rate MSE = 0.012).
• Compared with RF and MLP, KAN substantially outperforms in pressure prediction and shows strong performance for flow rate.
• Symbolic formulas extracted from KAN provide interpretable relationships between inputs and outputs (e.g., nonlinear influences of voltage, channel height, and gaps on pressure; apex angle, electrode overlap, and gap on flow rate).
• Table I shows model MSEs: KAN (Pressure 12.186, Flow Rate 0.012); RF (Pressure 1750.017, Flow Rate 0.040); MLP (Pressure 78.329, Flow Rate 0.002).
• The study demonstrates KAN’s accuracy and interpretability as a tool for design and optimization of flexible EHD pumps.