I am reading a paper on genetic programming by Lipson and Schmidt called "Distilling Free-Form Natural Laws from Experimental Data" at the following link: https://science.sciencemag.org/content/324/5923/81/tab-figures-data.
- It's unrelated to the question, but the paper describes how to use experimental data to derive the laws of physics through a machine learning method called genetic programming.
In this paper, the authors claim "If our experiments collect time-series data, we can estimate the partial derivative between any pair of variables by taking the ratio of their numerical derivatives over time". Here is a screenshot of the paragraph and respective "PDE". authors' statement on PDE derivation; includes PDE equation
Equation: \begin{align} \frac{\Delta x}{\Delta y} \approx \frac{dx}{dt} / \frac{dy}{dt} \end{align}
This confuses me. I have taken multivariable calculus and a class on ODEs, and I use PDEs in physics, but I have never heard someone define a partial derivative as a "ratio of two ordinary derivatives". Is this actually a partial derivative?