Examples

Preamble

import numpy as np
from pysr import *

We'll also set up some default options that will make these simple searches go faster (but are less optimal for more complex searches).

kwargs = dict(populations=5, niterations=5, annealing=True)

1. Simple search

Here's a simple example where we turn off multiprocessing, and find the expression 2 cos(x3) + x0^2 - 2.

X = 2 * np.random.randn(100, 5)
y = 2 * np.cos(X[:, 3]) + X[:, 0] ** 2 - 2
expressions = pysr(X, y, binary_operators=["+", "-", "*", "/"], **kwargs)
print(best(expressions))

2. Custom operator

Here, we define a custom operator and use it to find an expression:

X = 2 * np.random.randn(100, 5)
y = 1 / X[:, 0]
expressions = pysr(
    X,
    y,
    binary_operators=["plus", "mult"],
    unary_operators=["inv(x) = 1/x"],
    **kwargs
)
print(best(expressions))

3. Multiple outputs

Here, we do the same thing, but with multiple expressions at once, each requiring a different feature.

X = 2 * np.random.randn(100, 5)
y = 1 / X[:, [0, 1, 2]]
expressions = pysr(
    X,
    y,
    binary_operators=["plus", "mult"],
    unary_operators=["inv(x) = 1/x"],
    **kwargs
)

4. Plotting an expression

Here, let's use the same equations, but get a format we can actually use and test. We can add this option after a search via the get_hof function:

expressions = get_hof(extra_sympy_mappings={"inv": lambda x: 1/x})

If you look at the lists of expressions before and after, you will see that the sympy format now has replaced inv with 1/.

For now, let's consider the expressions for output 0:

expressions = expressions[0]

This is a pandas table, which we can filter:

best_expression = expressions.iloc[expressions.MSE.argmin()]

We can see the LaTeX version of this with:

import sympy
sympy.latex(best_expression.sympy_format)

We can access the numpy version with:

f = best_expression.lambda_format
print(f)

Which shows a PySR object on numpy code:

>> PySRFunction(X=>1/x0)

Let's plot this against the truth:

from matplotlib import pyplot as plt
plt.scatter(y[:, 0], f(X))
plt.xlabel('Truth')
plt.ylabel('Prediction')
plt.show()

Which gives us: