Error propagation in a differential model

[loganirado]

Hello, I'm interested in using the tool to calculate error propagation from parameter uncertainty in the prediction capabilities of a differential model. I assume it would be similar to the Ishigami example, but the function would also depend on time.

Is there any example that covers this application? If not, would you be able to provide a quick description about how UQpy could be used for such purpose?

One could use the cup of coffee problem from Uncertainpy as a benchmark:

def coffee_cup(kappa, T_env):
    # Initial temperature and time array
    time = np.linspace(0, 200, 150)            # Minutes
    T_0 = 95                                   # Celsius

    # The equation describing the model
    def f(T, time, kappa, T_env):
        return -kappa*(T - T_env)

    # Solving the equation by integration.
    temperature = odeint(f, T_0, time, args=(kappa, T_env))[:, 0]

    # Return time and model output
    return time, temperature

Thanks in advance!