Your concerns are certainly legitimate, and I'm sure there are some situations where they apply. However, in many physical sciences (I would venture to say the vast majority), simulations are not chaotic. They are based on stochastic models that have converging behavior. So, in general, it really is fair for most people to rely on the stability of the simulations.
As for your other points, the issue of simulation accuracy is already taken very seriously in the areas where I've seen it used.
Let me give an example from my field (high energy physics). The pre-eminent event generator of choice is called PYTHIA. It incorporates as much known physics as possible, and is continually updated. There are groups that regularly convene to compare the distributions it produces to those seen in real experiments and adjust the parameters to improve the results. The code is open source, so you can readily make improvements and submit them to the maintainers for inclusion in official releases.
Now the primary uses of these simulations are to either tune your analysis to separate signal from background or calculate corrections for different kinds of detector acceptance issues. No reviewer would ever accept a publication that used simulation if the paper did not include clear evidence that the simulation was valid, usually in the form of a data/simulation comparison.
Regarding reproducabilility, I think you're a little off the mark. The idea is not that you should simply repeat my analysis to get the same answer (this important verification step should be, and usually is, present in all scientific groups). Ideally, you should collect your own data, make your own simulations, and do your own analysis. Then we should see if we got the same answer.
"As for your other points, the issue of simulation accuracy is already taken very seriously in the areas where I've seen it used.... my field (high energy physics)"
Bad example, inasmuch as it is too good. Particle physics has petabytes of data (exabytes yet?) to test against and is very connected to the real world. With that check you can't stray very far.
"Ideally, you should collect your own data, make your own simulations, and do your own analysis. Then we should see if we got the same answer."
I would say a precondition of that step is first that I can reproduce your work. If I can't even reproduce your computation it's not even worth trying to reproduce the eventual results, as your eventual results are too questionable to begin with, as far as I am concerned. If I can't reproduce the computation you might as well have just pulled them from your bum.
Weather simulations have even more data; they are less accurate for other reasons.
Also, running someone else’s exact simulation again is useless. You need to start from scratch (or some vary well accepted baseline libraries) for it to be useful.
"Weather simulations have even more data; they are less accurate for other reasons."
I doubt anyone can beat particle physics for sheer information quantity. I seriously doubt that we have petabytes of real weather information to feed our simulations. I can find some references online to petabyte stores for weather simulation results online, but that's ultimately just cache, not information (in the information theoretic sense).
This is part of what I mean when I talk about the information theory, and how you can't get more information in the information-theoretic sense than the sum total of the simulation and the original data. Weather simulations may chew through terabytes or petabytes of RAM in the simulation phase, but they are not fed that much data. If the people involved mistake it for real information, then this is also part of what I mean when I say that once you get into using computers in a big way my training does indeed start giving me standing to complain again by even the most rigid "stay out of my science" standards.
Secondly, your assumption that running the simulation again is useless in a world where you can casually assume that you have all the data and the simulation and can have the contempt bred of familiarity for the whole process. In the real world, if you can't replicate the results, how can you criticize the model? I think there's still some "the computer said it, it must be right" underlying your answer; you can't assume the computer model is worth anything, it must be proved and debated and peer reviewed, which is not possible if you can't even get it to run and get the same results. The model is still subject to scientific inquiry, it can't be given a free pass.
Independent replication of results is also desirable, but you need both. In a world where nobody can replicate the results and it's hard to verify the simulation against the real world, it's too damned easy to end up with the Feynman electron mass situation where the selection effects from the researchers dominate the putative results of the simulations. The researcher summaries of the results of some runs of some models you can't see or execute and some data you can't get at happen to align... what does it mean? Frankly, who knows?
Several satellites take high resolution real time pictures of global weather they run 24 x 7 for years and that's RAW data. There are several of these plus radar stations etc. NOAA uses a subset of that information to make weather forecast (they normally toss out old data and data from the other side of the planet because it's not useful even if it might make a slightly better forecast). We can make highly accurate block by block forecast an hour ahead over major cities and just about any point in the US. However, there is little point in reading that level of detail from a forecast for such a short period of time. Sometimes when the forecast is 50% chance of rain over the next 8 - 12 hours they know where and when it's going to rain they just don't know where you are.
edit: One of the world's largest scientific data systems, NASA's Earth observing system data and information system (EOSDIS) has stored over three petabytes of earth science data in a geographically distributed mass storage system. that's just Nasa and a lot of their data does not make it into EOSDIS.
The goal of science is to understand the world. Running the same simulation on the same data and getting the same result only tells you that the machine running the simulation is not broken. What you want is to run a different program with different assumptions on different data and come to the same conclusion. This is actually used to make 7 day forecasts. They run a few different models with different assumptions and pick the average result. Over time each model is updated independently to maintain its independence.
PS: You don’t validate E=MC^2 by doing the exact same experiment 10,000 times. You do every type of experiment that you can think of which relates to E=MC^2 looking for anything which does not work out the way you think it should.
I think this ongoing discussion is fascinating, and I don't disagree with you.
But (and you knew that was coming), re-running someone else's code, or reproducing someone else's experiment is verification. It doesn't mean that what they did is valid, but it verifies that they did do what they said they did.
As for your other points, the issue of simulation accuracy is already taken very seriously in the areas where I've seen it used.
Let me give an example from my field (high energy physics). The pre-eminent event generator of choice is called PYTHIA. It incorporates as much known physics as possible, and is continually updated. There are groups that regularly convene to compare the distributions it produces to those seen in real experiments and adjust the parameters to improve the results. The code is open source, so you can readily make improvements and submit them to the maintainers for inclusion in official releases.
Now the primary uses of these simulations are to either tune your analysis to separate signal from background or calculate corrections for different kinds of detector acceptance issues. No reviewer would ever accept a publication that used simulation if the paper did not include clear evidence that the simulation was valid, usually in the form of a data/simulation comparison.
Regarding reproducabilility, I think you're a little off the mark. The idea is not that you should simply repeat my analysis to get the same answer (this important verification step should be, and usually is, present in all scientific groups). Ideally, you should collect your own data, make your own simulations, and do your own analysis. Then we should see if we got the same answer.
Edit: grammar