Formula Finder - v0.1 Alpha

Non-linear curve fitting through use of Genetic Algorithms.

🔎 Feed it the data -> Pull out the formula ✨

Why build this?

I've recently been working on a small research paper, and wondered if GA could smartly speed up the process of Formula Hacking.

To my surprise, this initial prototype is able to extrapolate a few known formulas fairly quickly. So I thought I might just open source this.

Hope you find this useful :)

Main Future Plans

Add knowledge of dimensions to data (e.g. mass, length, time, etc) for better fitting
Add support for more complex functions
Improve config and test further mutation strategies
RNNs

Examples

Go to the Jupyter notebook Getting Started here for a list of examples

Example: Newton's Universal Law of Gravitation (with added noise)

Here below we mock some test data to pass to the algorithm, with some added noise.

from formula_finder import run_formula_finder

mass_earth = c.M_earth.to(u.kg).value # in kg
mass_sun = c.M_sun.to(u.kg).value # 
distance_earth_sun = 147e9 # in meters

xdata = np.linspace(0.8, 1.3, 20) * distance_earth_sun # x axis for distance
dim1_data = np.linspace(0.8, 1.2, 20) * mass_earth # variations of mass
dim2_data = np.linspace(0.8, 1.2, 20) * mass_sun # variations of mass

def ydata(data):
    # test data with noise
    return c.G.value * (data[1] * data[2]) / np.power(data[0], 2) * np.random.uniform(0.95, 1.05)


g, formula = run_formula_finder(
    num_generations=1000,
    comparison_func=ydata,
    xdata=xdata,
    dim1_data=dim1_data,
    dim2_data=dim2_data,
    dimension_names=["r", "m1", "m2"],
)
formula
>>> 6.6743e-11 * m1 * m2 / r ** 2

TODOS:

Better strategies at preventing evolution staleness
Explore RNNs to either replace or add to the algorithm
Usage on practical cases using either astrophyics or other areas where curve fitting is needed