specification_oscillator2_numpy.txt

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


import numpy as np

#Initialize parameters
MAX_NPARAMS = 10
PRAMS_INIT = [1.0]*MAX_NPARAMS


@evaluate.run
def evaluate(data: dict) -> float:
    """ Evaluate the equation on data observations."""
    
    # Load data observations
    inputs, outputs = data['inputs'], data['outputs']
    t, x, v = inputs[:,0], inputs[:,1], inputs[:,2]
    
    # Optimize parameters based on data
    from scipy.optimize import minimize
    def loss(params):
        y_pred = equation(t, x, v, params)
        return np.mean((y_pred - outputs) ** 2)

    loss_partial = lambda params: loss(params)
    result = minimize(loss_partial, [1.0]*MAX_NPARAMS, method='BFGS')
    
    # Return evaluation score
    optimized_params = result.x
    loss = result.fun

    if np.isnan(loss) or np.isinf(loss):
        return None
    else:
        return -loss



@equation.evolve
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