Function Discovery for Oridinary Differential Equation

Problem

The Ordinary Differential Equation (ODE) Function Discovery problem focuses on identifying functional relationships by minimizing mean square error using given X values and constant parameters.

• Given: X value, a set of constant parameters.

• Objective: Minimize the mean square error.

• Constraints:

  • None

Algorithm Design Task

• The task is to design the function to fit the dataset.

  • Inputs: X value.

  • Outputs: Predicted y value.

Evaluation

• Dataset: Dataset from ODEFormer: Symbolic Regression of Dynamical Systems with Transformers.

• Fitness: Mean Square Error

Template:

template_program = '''
import numpy as np

def equation(x: float, params: np.ndarray) -> float:
    """ A ODE mathematical function    
    Args:
        x: the initial float value of the ode formula
        params: a 1-d Array of numeric constants or parameters to be optimized

    Return:
        A numpy array representing the result of applying the mathematical function to the inputs.
    """
    y = params[0] * x + params[2]
    return y


'''

task_description = "Find the ODE mathematical function skeleton, given data on initial x. The function should be differentiable, continuous. Only selectable components: 1. Basic operators: +, -, *, /, ^, np.sqrt, np.exp, np.log, np.abs 2. Trigonometric expressions: np.sin, np.cos, np.tan, np.arcsin, np.arccos, np.arctan 3. Standard constants: 'np.pi' represents pi and 'np.e' represents Euler's number"