To find a scientific definition of supernatural it is necessary to start with a standard dictionary definition of supernatural. According to The American Heritage® Dictionary of the English Language the primary definition of supernatural is “Of or relating to existence outside the natural world.”
Since the natural world consists of ther entire universe, it is logical to rephrase this definition as “Of or relating to existence outside the Universe.” This makes for a perfect scientific definition of supernatural.
So here is a perfect scientific definition of supernatural.
Supernatural: Of or relating to existence outside the Universe.
Supernatural event: Aany event that has a caused out side the Universe.
Now while this definition allows for an influence by a supernatural intelligence such as God, it does not intrinsically require that there be any intelligents involved an would include totally mechanistic causes from out side the universe.
Reference Science and the Supernatural