A probabilistic comparison of the models, e.g. involving some likelihood computed from the $\epsilon$ with some data (and derived from this AIC or ratio test), makes little sense.
This is because
- You already know for certain that the model is gonna be wrong.
- The residuals that you end up with have no relation with the hypothesised distribution of errors that you use to test different hypotheses. (you do not have a statistical/probabilisitc model)
- Your goal is not to test a hypothesis, but to characterize the prediction performance of a simplified model.
Most often people describe models in terms of the percent of error for predictions.
Examples:
It is shown that these correlations can be used to predict pressure drop to within ±20% for a given sludge concentration and operating condition.
The present model suits with the 501 viscosity values with mean deviations lower than 5% and 75% of them are within the correlation coefficient 0.78–1.
Figure 2 presents a comparison between measured viscosity ($\rho$) and the viscosity calculated by Einstein model. A difference between calculated and measured values confirms that there is an elevated physical interaction between asphalt base and rubber particles.
A correlation coefficient (r2) of 0.94 was determined for the relationship between known LWAPCs (log water‐to‐air partition coefficients) and bond estimated LWAPCs for the 345 compound data set.
Basically you can google any model that is a simplification of reality and you will find people describing their discrepancy with reality in terms of correlation coefficients, or percent of variation.