introduce specific expressions in the inital population

[AKHCE]

Hi,
I am wondering if we can tell pysr that include specific expressions in the inital population. E.g. assume : I know that three expressions y=x1**2+1, y=x**1.5+2, and y=exp(x1/10)/5 could kinda be close to the final solution, and I am interested that pysr includes these specific epxressions in the initial population. Is there any built-in feature in pysr to address such a request?

Any advice is much appreciated.

[MilesCranmer]

See:

• Start search from a base function #418
• Create Hall of fame manually #443

[riccardocappi]

Hi everyone, I'm new to PySR and I'm also interested in introducing specific expressions into the initial population. I saw the previous discussion on this topic, but I’m hoping for an easier way to do it or any new insights. Any guidance would be appreciated.

[MilesCranmer]

@riccardocappi now there is sort of an easier way to do it via template expressions:

expression_spec = TemplateExpressionSpec(
    expressions=["f", "g"],
    parameters={"a": 1},
    variable_names=["x"],
    combine="""
        y1 = (x + f(x))^2 + 1 + a[1]
        y2 = exp((x + f(x))/10)/(5 + a[1])
        g(x, y1, y2)
    """
)
model = PySRRegressor(expression_spec=expression_spec, **kwargs)

Basically this is creating a hierarchical expression where f and g are learned expressions, and a[1] is a learnable constant.

So this model could choose to have f = 0.0; g = #2; a = [0.0], in which case the result would be equal to y=x**2+1. OR, it could learn f = 0.0; g = #3; a = [0.0] in which case the result would be equal to y = x**1.5 + 2.

But it could also learn something like f = #1; g = #2; a = [1.5] which is equivalent to y = (2*x)**2 + 2.5`.

it could also learn something entirely different like f = 0.0; g = cos(#1); a = [0.0] which would just be y = cos(x).

But you can see how it is "easier" for the model to find something like @AKHCE's original suggested expressions; while still allowing the model to learn something arbitrary.

[riccardocappi]

Thank you for the quick reply!!

So, let's assume that I have to learn the ground truth function f = 1.5 * sin(x0 - x1). I have obtained from another optimization procedure (not with PySR) the function f_init = 1.2 * sin(1.01 * x0 - 1.02 * x1) + 0.03 * x0. My goal is to provide the latter expression as initial condition to PySR to speed-up the fitting (and hopefully obtain a more precise result).

According to your answer, I can replace the coefficients of f_init with some parameters a[1], a[2], ... and let the model learn the correct ones through the TemplateExpressionSpec method. However, i'm wondering if with this method the model is able to get rid of 0.03 * x0, which appears in f_init but not in the ground truth function.