On some temperatures, our linear models fail, for example water cooled below 4 degrees Celsius will not continue to get denser, but it will actually expand, allowing the cold water to float on the surface until it becomes ice. In general, lower temperature would predict lower density in substances. There is nothing in the common physical laws that would predict such anomaly in water, while we can later construct even more complicated models to explain what is happening with water.
The way fluids and air flows near solids is also very hard to model. The "Coanda effect" is not easily derived from the usual physical laws. We have some laws about fluids like Bernoulli principle, however this only holds for very narrow ranges of parameters. Very small pipes shows capillarity effects that are not predicted from Bernoulli models. Aircraft flight is not correctly modeled only from the Bernoulli equations.
We just find better and better approximations of reality, however not a single model can explain all the complexity we encounter. Even if we take the very basic laws we have about electrons and protons, and we would apply a huge amount of calculation, I am sure that we will not be able to derive all we can observe.
We still struggle to understand why protons stay together in the nucleus, while our electromagnetic model predicts that they should repel each-other. We have a separate models also for this situation, however the unified model that should also explain gravity is still out of reach.
String theory tries to model everything, by using such small modelling "bricks" that you can actually approximate anything. But is this the model from where we can derive all the other laws? For now it looks more like a very complicated model that only tries to approximate things that cannot be easily approximated by the previous models.
Either or not there is an unifying theory that will explain the whole Universe is still to be decided. Until then, we still believe in a very compressible Universe, that can fit in our limited brain.
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