One of the puzzles in the scientific explanation literature is how it is that one can genuinely have explanation in the special sciences—chemistry, biology, geology, etc.—given that the facts in the purview of the special science in question appear to reduce to facts of physics, and hence it seems that only physics-based explanations are appropriate. One strategy is to resist the reduction move. I am happy to resist the reduction move for biology, but to me reduction seems exactly right for geology and probably for chemistry.
The theist, however, has a neat story, like the one in my previous two posts. The patterns that the special science identifies are valuable. They are valuable intrinsically—they exhibit an aesthetic good (and scientists talk of the beauty of theories, though admittedly they do so less in the special sciences)—and they are valuable instrumentally as they make it possible for us to make predictions and organize our knowledge. Because these patterns are valuable, God intends them and their presence is causally explicable. This holds whether or not the given generalization in the special sciences rises to the level of laws or not.
What happens, though, when one pattern is subsumed into a wider pattern? As long as the narrower pattern is still there, it can be correctly used for explanation. But explanation in terms of the wider pattern is better, because the wider pattern is more valuable, and hence more explanatory of God's creative action. Thus, early on we may have learned that all mammals have hearts, and later on we learned that this is true of all vertebrates. It is still correct to explain the presence of the heart in Socrates by his mammality, but better to do so by reference to his being a vertebrate.
A similar move explains why it is that when there are two formulae that equally fit all the data, the simpler is the one to be preferred in explanation. This is relevant to both the curve-fitting problem and the problem of which of two mathematically equivalent formulations is the more explanatory.
Furthermore, that some simple theory approximately fits a body of phenomena is also of value. Hence, theories that are mere approximations can yield genuine explanations. And that is how it should be. In particular, Newtonian mechanics continues to be explanatory, and not simply because of classical-limit stuff in quantum mechanics.
The theistic story also explains why it is that Lagrangian mechanics was genuinely explanatory, despite not fitting well in the mechanistic model of explanation. This is, of course, an application of Leibniz's discussion of teleological explanation.