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GMDH decomposes the complexity of a process into many simpler relationships each described by low order polynomials (2) for every pair of the input values.
Within a given platform, the σ plots have similar general shapes that can be fitted well by low order polynomials.
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By choosing low order polynomials for representing the curvature radius functions, the interpolating curves can be spirals that have monotone curvatures or fair curves with small numbers of curvature extremes.
The control variables are then approximated within each interval by means of low order polynomials.
In these subdomains local basis functions, for instance low order polynomials, are defined and the original PDE is approximated by N ordinary differential equations (ODE).
The functions (d_{i}) ((i=1,2,3)) are low order polynomials and can be explicitly evaluated.
For example, we tried fitting low order polynomials to division rates over time, but the fits were unsatisfactory, as judged by assuming counts were Poisson distributed with rates predicted from the polynomial fit.
The control vector parameterization proceeds dividing the process duration into a number of elements and approximating the control functions typically using low order polynomials.
The use of appropriate mappings within each subdomain can improve the accuracy of the approximation by choosing mappings so that the transformed function is more readily approximated by a low order polynomial.
It was also shown that if there are equal children emanating from each node in this tree structure, the number of levels of the tree is logarithmic in the number of users and the complexity is bounded by a very low order polynomial in n.
So the key thing to take away from these graphs is that, a very low order polynomial is really too simple.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com