System that is more efficient to simulate than to compute I know some physics calculations require alot of computing to solve.
Are there currently systems where it is more logical to do an experiment to "let the universe simulate the experiment for us" and measure the outcome instead of calculating it out of time/resource concerns?
Note i do not mean the complexity of the experiment or number of independent variables but solely out of a mathematical standpoint.
 A: Virtually all experiments (at least in condensed matter physics) fall under this category.  Unlike in high energy, where we're actually testing fundamental physical theories, at the energy scales of condensed matter, we are quite confident that in principle, the many-body nonrelativistic Schrodinger equation runs the whole show.  (Perhaps with relativistic corrections in the case of the heavier atoms, where spin-orbit coupling can be significant.)  In Dirac's famous words, "The underlying physical laws necessary for the mathematical theory of a large part of physics and the whole of chemistry are thus completely known, and the difficulty is only that the exact application of these laws leads to equations much too complicated to be soluble."  Since we can't solve the $10^{23}$-body Schrodinger equation, we still do experiments.  (This is even more the case in the case of cold atoms, where we can precisely control the Hamiltonian itself, but the field of cold atom experiment is flourishing.)
A: A very well-known example is atomic weapons.  It is much easier to build a device and test it than it is to simulate it: it took a very long time before simulations of existing designs and small variations on them became convincing enough that people had any faith in them at all, and I believe that we can really only use simulations now because it became clear that small variations on existing designs were adequate, and radical innovations were no longer needed (no-one wanted suitcase nukes or hundred-megaton devices to exist).  Even now there are many physical tests of critical aspects of weapon systems (some of this sort of thing goes on at the National Ignition Facility).
Of course full tests of nuclear weapons have several undesirable side-effects, so people were eventually pushed into simulations combined with physical tests of things that were too hard to simulate.

More generally almost any complex system -- which is almost any system -- is generally either ludicrously hard or completely impractical to simulate numerically.
More generally still, if you are just doing simulations, you're not actually doing physics: you're testing a model you've made, which can be interesting in itself, but to do physics you need to be comparing the model with the world.
