Kolmogorov-Arnold Model

This is a quick testing tool for a new data modeling technique introduced by Mike Poluektov and Andrew Polar. Users can upload their own data as semicolon separated numbers and see the accuracy of the model. The data is parsed and processed by JavaScript code in this HTML file. The code can be seen by 'View Page Source' option of the browser. It can be saved to file, retained and modified.

The used model is Kolmogorov-Arnold representation for multivariate function $G$

$$ y = G(x_1, x_2, x_3, ... , x_n) = \sum_{i=0}^{2n} \Phi_i \left(\sum_{j=1}^{n} f_{i,j}(x_{j})\right), $$

where parameters $x_j$ are inputs, $y$ is a target of modeling and set of functions $f_{i,j}$ and $\Phi_i$ constitute the model. This model is considered by authors as alternative to neural networks. Provided list of data sets with inputs and corresponding targets, the suggested method builds all involved functions not in parametric form but by constructing of their actual shapes. The model functions are continuous and piecewise linear, and the only parameter that user needs specify is number of points per function.

The theoretical concept is published:
  • M. Poluektov, A. Polar. Modelling non-linear control systems using the discrete Urysohn operator. Journal of the Franklin Institute. Volume 357, Issue 6, April 2020, Pages 3865-3892.
  • A. Polar, M. Poluektov. Patent application #20200050649. Method for Identifying Discrete Urysohn Models. Filed on 08/11/2018.
  • A. Polar, M. Poluektov. A deep machine learning algorithm for construction of the Kolmogorov-Arnold representation. Jun. 23, 2020. arxiv.org/abs/2001.04652
  • Nonlinear Adaptive Filtering
  • A. Polar, M. Poluektov. Patent application 16/781,657. New form of artificial intelligence and training method thereof. Filed on 02/04/2020.
Before uploading your data we recommend to use one of those datasets that people use for benchmarks. They can be downloaded from provided links.
This file contains experimental data for the physical object. Obviously, the choice of parameters, measurement errors and other natural factors are the reasons for model discrepancy. The accuracy matches reports of modeling of this same data by neural networks. Airfoil self noise

This is the file with 5 random inputs and output computed by formula. The formula has no physical meaning, it is only the challenging algebraic expression:

$$y = \frac{|{sin(x_2)}^{x_1}-1/e^{x_3}|} {x_4} + x_5 \cdot cos(x_5)$$


Use controls on the left to upload your data. After data is processed and model is built, the accuracy is reported by Pearson correlation coefficient, computed for target $y$ and model $\sum_{i=0}^{2n} \Phi_i \left(\sum_{j=1}^{n} f_{i,j}(x_{j})\right). $ In order to repeat computations, browser 'reload' must be used.