Math Knowledge Discovery for Oscillator2

Problem

The Oscillator2 problem, introduced in LLM-SR: Scientific Equation Discovery via Programming with Large Language Models, is a mathematical exploration task focused on identifying oscillator patterns by minimizing mean square error with given environmental parameters.

• Given: Environment parameters, 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: Time, current position, velocity, numeric constants or parameters to be optimized.

  • Outputs: Predicted value.

Evaluation

• Dataset: Dataset from LLM-SR: Scientific Equation Discovery via Programming with Large Language Models.

• Fitness: Mean Square Error

Template:

template_program = '''
import numpy as np

def equation(t: np.ndarray, x: np.ndarray, v: np.ndarray, params: np.ndarray) -> np.ndarray:
    """ Mathematical function for acceleration in a damped nonlinear oscillator
    Args:
        t: A numpy array representing time.
        x: A numpy array representing observations of current position.
        v: A numpy array representing observations of velocity.
        params: Array of numeric constants or parameters to be optimized

    Return:
        A numpy array representing acceleration as the result of applying the mathematical function to the inputs.
    """
    dv = params[0] * t + params[1] * x  +  params[2] * v +  + params[3]
    return dv


'''

task_description = "Find the mathematical function skeleton that represents acceleration in a damped nonlinear oscillator system with driving force, given data on time, position, and velocity."