Is conservation of energy a concept developed out of experiments or can it be derived out of any theoretical model (like Newtonian mechanics or general relativity)?

All physical laws, including the principle of conservation of energy, are ultimately derived from observation . One can't conclude anything about the empirical world purely from reason or mathematics. You always need a set of empirical facts. Noether's theorem shows that time translation symmetry gives rise to conservation of energy. Whenever a system is invariant under time translation, its energy remains constant over time. It is a mathematical theorem linking two apparently separate ideas. If the former is true then the latter must be true. But it can't say whether any of them is true or not in our world. You need to observe the world to know that. In general relativity for example, the global conservation of energy is a problematic concept.

Conservation of energy is a concept developed out of experiments. The whole branch is called thermodynamics. There has been no violation, observed, as long as you remember the inter-convertibility between mass and energy. Thanks for the A2A.

A physical theory, and also the postulates on which it is based can only be validated, that means that every experiment done shows that the theory holds and in this case energy conservation holds. A physical theory can be proven only to be false even by one datum, and then the theory changes. Though Noether's Theorem can give you a rigorous mathematical proof. But it's assumptions applying on the observations I make irritate me a bit. So I would be happy to accept it as an axiom rather than a derived law.

It is a concept developed out of experiments and observations and can be derived theoretically also, like the Work-Energy theorem.