Likelihood function in bayes by backprop

Question

I generate my regression data synthetically using finite element method. So inherently my synthetic data is noiseless. In this case can someone help me understanding how can I write my likelihood function? (Likelihood term of my ELBO)

I have seen common use of following negative log likelihood function, how one can choose value for standard deviation here?

def neg_log_likelihood(y_true, y_pred, sigma=noise):
    dist = tfp.distributions.Normal(loc=y_pred, scale=sigma)
    return K.sum(-dist.log_prob(y_true))