In nearly all situations, these advanced calculations bear only a limited relationship to the underlying physics occurring in material systems. A lot of simulation work involves twiddling parameters until you get the result you want to see, and then just publishing that one simulation. It's sort of a post-hoc retro-causality problem. Many of the things you describe came about because of a combination of immense amounts of lab work (mostly of which were failures), some theoretical concepts, and a person willing enough to twiddle params until they fall up something that works, after which they can optimize the parameters.

It is true that simulations produce results which may not reflect the underlying system if the simplifications and fudge factors are incorrect. Thus fiddling with parameters is part of the process.

In the example I gave of searching for zeolite catalysts, the simulations were just used to identify candidates for labs to study. I don't remember the exact numbers, but I think it brought the list of candidates down from hundreds to less than 10. The majority of these candidates were at least somewhat effective. Unless we believe that pretty much all of those hundred candidates would have been effective, then the advanced calculations were doing some work.

The question is, is all that work actually just done because of parameter twiddling? I don't think so. Consider that neural networks are often used lately in order to provide computationally simpler models of various physical phenomena. They can do a somewhat better job if fed with a lot of real data, but they use at least thousands of times more parameters than the simple quantum physics calcs with fudge factors. Thus I think it is safe to say that the structure of the quantum physics calcs does meaningfully model some part of reality. (Unless, as xvector points out, our memories are being continuously overwritten to make reality seem consistent)

It's also good to note that the fudge factors (read: parameters) and quantization are done because it would be too computationally difficult to model the parts of the system modeled by fudge factors for systems with a useful amount of atoms in them, and we just don't know how to compute ODEs for complex systems in continuous time and space. In simple systems, (e.g. 2 photons interacting) analytical solutions for ODEs can be found, no fudge factors are needed for computation, and the computed results match the experimental results to within measurement error.

> Basically, I believe the advanced calculations to be correct because they lead to things which are (eventually) used in daily life.

I think you are missing my point - if you can short circuit logic, you will never be able to know whether your calculations are correct (but you will believe it)

Whether the outputs are used in daily life or not is irrelevant. You don't truly know if that is happening because you do not know what the fuzz factor is in the simulation.

Is the night sky the same as it was yesterday, or is it generated on the spot and your memory edited? The latter is more compute efficient.

Does your coworker look the same, or is the fuzz factor in the sim very high and they have a new face/body generated every day, with your memory edited to match?

Etc. that the outputs of the equations you described are used or not is irrelevant because it would be far more compute efficient to just not have them mean anything and to fuzz their existence/workability

Indeed, I can't prove that it is or isn't the case that my thoughts and memories aren't being constantly overwritten to make reality consistent. I don't have a firm belief one way or the other, but I act like reality does intrinsically make sense.

Reason being, if reality is consistent, than acting as though it does achieves my goals. If reality isn't consistent, or is consistent in a way that differs from what I am capable of comprehending, then I am unable to compute any pattern of behavior that would be helpful to achieving my goals.

Thus it only makes sense to me to act like reality is consistent. I think that if I am acting this way, then it makes sense for me to say that I "believe" reality is consistent in a non thought overriding way.

EDIT: Looking at your comment again, I think that you think it is likely that reality should be simple because computing that would be easier. If we are stuck in a simulation by more advanced beings, then it is possible that compute power is a limiting factor, or they may just have computers so powerful that simulating us could be a cinch.

The simulation scenario is easy to imagine. However, just because I can't imagine scenarios besides "it just is this way", "God did it", and "We are in a simulation" doesn't mean such scenarios don't exist.