If summarizing stats from multiple models is it meaningful to report a mean AIC? I am currently summarizing results from several groups of models.  
Is it meaningful to report a mean AIC for each group of models?  If not then how best to give a summary measure for each model group?
Some contributing factors


*

*all models have the same number of parameters and structure 

*within each group, there are four models, which always have the same numbers of data points.  e.g. each group has always contains four models with 50, 60, 80 and 100 data points respectively.


UPDATE
I haven't had any responses yet, but I have had further thoughts on this matter.
How do we define "meaningful"?  In this case it's probably best to think in terms of what we will do with the results, the mean AIC.  Interpretation of AIC is usually through likelihood function, which gives the likelihood that the worse of a pair of models is actually better (and the measured AIC difference between them is down to chance):
$\mathcal{L} = e^{-\frac{1}{2}|\Delta AIC|}$
Where $\Delta AIC$ is the difference in AIC between the models.
Without loss of generality, consider the case where we take the mean of two AICs, $\overline{AIC} = \frac{1}{2}(AIC_1 + AIC_2)$, and compare them to a bassline model which has $AIC_B=0$ while $AIC_1 > 0$ and $AIC_2 > 0$.  Then we interpret the mean as a single AIC and apply the formula for $\mathcal{L}$:
$\mathcal{L}(\overline{AIC}) = e^{-\frac{1}{2}|\overline{\Delta AIC}|} = e^{-\frac{1}{2}\frac{1}{2}(AIC_1 + AIC_2)} = \sqrt{e^{-\frac{1}{2}AIC_A}e^{-\frac{1}{2}AIC_B}}$
which is the geometric mean of $\mathcal{L}_1 = \mathcal{L}(AIC_1)$ and $\mathcal{L}_2 = \mathcal{L}(AIC_2)$.  So far so good: it makes sense to compute an arithmetic mean of AIC if it makes sense to compute a geometric mean of $\mathcal{L}$.  (I would like to say "if and only if" but that would preclude any rationalization for doing this outside of the current argument.  In the current line of thinking though this is an "iff").
So does it make sense to compute a geometric mean of $\mathcal{L}$?  Presumably the reason for averaging in this manner is that we're trying to compute the expected $\mathcal{L'}$ that you will get if you apply a similar model to another dataset in future.  In this case we need to look at $E(\mathcal{L'})$ the expected likelihood, assuming equal probability of each model within the group.
$E(\mathcal{L'}) = P(\mathcal{L}_1)\mathcal{L}_1 + P(\mathcal{L}_2)\mathcal{L}_2 = \frac{1}{2} \mathcal{L}_1 + \frac{1}{2} \mathcal{L}_2 = \overline{\mathcal{L}}$
This is the arithmetic, not geometric mean of $\mathcal{L}_1$ and $\mathcal{L}_2$.  So no, it doesn't make sense to report the arithmetic mean of the AIC, because it doesn't make sense to report the geometric mean of $\mathcal{L}$.  
Conversely, it would make sense to report the arithmetic mean of $\mathcal{L}$, so that would be a sensible way to summarize a group of models.
If anyone feels like answering it would still be useful to receive comment on the correctness (or disastrous incorrectness!) of this analysis.  I am not very sure of the latter part of the argument, as $\mathcal{L}$ is a relative likelihood perhaps it is appropriate to take the geometric mean anyway?
 A: I think that you can use median or average AIC of a group of models in comparison to another group for internal analysis or during the selection of model specifications for further consideration. There is an interpretation of the difference between AIC of two models in terms of likelihoods, see here. In a similar somewhat informal way you could compare the groups of models represented by their summary AIC. 
A: There is no real meaning in combining AICs.  There is sometimes (seldom) benefit from combining models, e.g., Bayesian model averaging or coefficient averaging, but I haven't seen anyone combine AICs.
You did not explain why you have more than one model in the first place.
A: In my humble opinion, summarizing/averaging AIC/BIC makes some sense (it is quite scary to me that I'm disagreeing on this with @Frank Harrell :-). At least, I've seen this being done and written about. Please see one of my earlier answers here on Cross Validated with more information and relevant references: https://stats.stackexchange.com/a/128922/31372.
