Do axioms exist in the natural sciences? Are the fundamental laws the axioms? E.g. principle of least action, conservation of mass/energy, etc.
A nice little book on this is "Scientific Method in Practice" by Hugh Gauch. He discusses the critical role of presuppositions in science. He also gives a nice overview of the Science Wars, which, among other things, made heavy use of the idea that science, like all other disciplines, requires presuppositions.
In regards to your question, Gauch gives what I think is the most fundamental presupposition/axiom of science, indeed, in all of rational inquiry:
The world is objective, orderly, and comprehensible
Some unpacking of defintions:
objective - this is bascially a statement of realism. Science presumes there is a single world "out there", independent of perspective or state of perception.
order - in the sense that there is a pattern to existence. It does not imply determinism, merely that there is some order imposed on the universe. E.g., the wave function itself is VERY ordered and puts rather precise restrictions on an experiment. However, it does not determine the outcome, in as much as there are a multitude of possiblities.
comprehensible - Humans have access (albeit imperfectly) to the objective world and have the ability to make reliable conclusions about it.