PySR symbolic regression

[pukpr]

Exploring the https://github.com/MilesCranmer/PySR site

Fitting to a QBO model with a Draconic forcing $x_1$ and time-base $x_0$,
Discovered that solutions of complexity 5 to 7 below have a frequency term (2.313618) that matches a sidereal cycle exactly

sidereal	27.321661554 + 0.000000217 × T

PySRRegressor.equations_ = [-----
            pick     score                                           equation       loss  complexity
        0         0.000000                                          19.750309  4097.2925           1
        1         0.048810                                   (26.180695 - x1)  3716.2168           3
        2   >>>>  0.102009                      ((-5.044393 * x1) + 52.20112)  3030.3823           5
        3         0.009072               (((-5.314505 * x1) + 2032.943) - x0)  2975.8975           7
        4         0.005377  (((-5.2127695 * x1) - -1284.6315) - (x0 * 0.62...  2944.0645           9
        5         0.028976  (((-5.0717497 - cos(x0 * -2.313618)) * x1) + 5...  2859.9817          10
        6         0.017240  (((-5.137973 - (cos(x0 * -2.313618) / 0.397038...  2763.0503          12
        7         0.001717  (((-5.141418 - (sin(cos(x0 * -2.313618)) / 0.3...  2758.3096          13
        8         0.004781  ((((-5.21715 - (cos(-5.137973 * x1) * -2.34991...  2745.1533          14
        9         0.004426  (((-4.888953 - (cos(-5.13929 * x1) * (-2.18357...  2733.0305          15
        10        0.003883  ((((-5.191417 - (cos(-5.2127523 * (x1 - 1.4107...  2722.4387          16
        11        0.017655  ((((-5.1426735 - (cos(-5.138464 * x1) * (-2.23...  2674.7960          17
        12        0.005303  ((((-5.0717497 - (cos(-5.1406274 * x1) * (-2.0...  2646.5771          19
        13        0.006679  ((((-5.253864 - (cos(-5.1370616 * x1) * (sin(x...  2628.9585          20

$$\frac{365.242}{\frac{2.3136}{2\pi} +13} = 27.32166 $$

2.3136	0.368221	13.36822	27.32166
term in rad	freq	aliased	period(days)

It has popped up elsewhere

10 2.860e+03 2.898e-02 y = (((-5.0717 - cos(x₀ * -2.3136)) * x₁) + 52.427)
12 2.763e+03 1.724e-02 y = (((-5.138 - (cos(x₀ * -2.3136) / 0.39704)) * x₁) + 52.472)
13 2.758e+03 1.717e-03 y = (((-5.1414 - (sin(cos(x₀ * -2.3136)) / 0.36216)) * x₁) + 52.398)

[pukpr]

comment at PySR

I have a set of what I would categorize as unsolved geophysics time series problems that I am modeling. The solutions I have found are all physics-informed but not necessarily well-accepted, even after publishing. Over the years, I have experimented with using symbolic regression to see if it could discover the same solutions, and I did find that Eureqa was very promising in being able to get close. I don't know what it is but Eureqa had some sort of special sauce to it; unfortunately it is out of commission these days.

But, if anyone is interested the problems that I am working on that could benefit from symbolic regression experimentation are:
Chandler wobble
Quasi-Biennial Oscillation (QBO)
El Nino Southern Oscillation (ENSO)
Atlantic Multidecadal Oscillation (AMO)
Indian Ocean Dipole (IOD)
Pacific Decadal Oscillation (PDO)
North Atlantic Oscillation (NAO)

There is a commonality to the physics-modeling approach I am using on all of these and so there is a strong possibility of cross-validation.

However, the sticky point in getting something like PySR to match is in first coercing it to it lock-in to the formulation I am finding. That''s why I haven't been using PySR as much as using custom software.

My suggestion as to how to proceed is to instead of providing the real data of QBO (for example) for PySR to fit to, instead to try to find out if PySR could fit to a model of QBO, which would be free of noise or other anomalies.

This would be huge if even a few of these problems could be solved, as the reality is that geophysicists and climate scientists really have little faith in their own models for the phenomena. Google, NVIDIA, and Huawei are spending millions $$ in research on the climate aspects to these time series, clearly concentrating on using neural networks to find something. However, unless they get the physics and especially the external forcings right, I don't think the NNs are going to find the solutions. That's because the solutions aren't found solely within the data but as a consequence of manipulating the external factors. And that's why I think symbolic regression approaches will work better.