Physics Knowledge Discovery for Stress & Strain

Physics Knowledge Discovery for Stress & Strain#

Problem#

The Stress & Strain problem, proposed in LLM-SR: Scientific Equation Discovery via Programming with Large Language Models, is a physics-based task that focuses on discovering relationships by minimizing mean square error using environmental parameters.

../../_images/stress.png

  • 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: Strain, temperature, 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(strain: np.ndarray, temp: np.ndarray, params: np.ndarray) -> np.ndarray:
    """ Mathematical function for stress in Aluminium rod
    Args:
        strain: A numpy array representing observations of strain.
        temp: A numpy array representing observations of temperature.
        params: Array of numeric constants or parameters to be optimized

    Return:
        A numpy array representing stress as the result of applying the mathematical function to the inputs.
    """
    return params[0] * strain  +  params[1] * temp
'''

task_description = "Find the mathematical function skeleton that represents stress, given data on strain and temperature in an Aluminium rod for both elastic and plastic regions."