I am trying to compute the derivative of the Lorenz system simulation with added white noise. For example, if I want to compute the derivative of x data w.r.t. the time t. The plot of x vs t is attached in figure_1.
I have intentionally added some noise to check the robustness of the derivative calculator on experimental data. So, I can't use numerical derivative techniques such as finite difference.
I chose polynomial regression with better-conditioned polynomials such as the Chebyshev polynomials for obtaining the polynomial equation and then differentiate it simply.
Of course, for such a complex curve, I need to do multiple local polynomial fittings to capture the sharp local changes in the curve.
However, I am obtaining really high values of the derivatives from the polynomial regression. Please have a look at the Python code. It would take 5min to run the code.
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