For Natural Science, please consult the attached entry of Wikipedia. Some, but not all, experimental sciences, such as Experimental Physics (link attached), fall in the category of Natural Sciences. There is for instance Experimental Psychology (link attached), which may at least partly be considered as Experimental Physics.
The term 'physical reality' unduly suggests existence of something concrete and knowable out there, while everything we know about the 'physical reality' is through our direct sense perceptions, or through a set of measurements that complement these perceptions. Scientifically, we make sense of these observations by building scientific models, all linked together by means of universal laws of physics that have been obtained, and continue to be obtained, through the process of inference. If we can describe all the physical phenomena that we observe by means of a set of laws that involve waves and probabilities, then so be it.
Incidentally, waves and probabilities are encountered also in classical physics. Think of waves in elastic media, and the classical Boltzmann and Maxwell distribution functions, which are probability distribution functions. Quantum mechanics was invented as a way out of a number of serious problems for which classical mechanics had no solution. You may be interested to know that one can bypass use of the quantum-mechanical wave functions by using the hierarchy of the Wigner distribution functions (consult the link attached below).
To summarise, the aim of science, and of natural science in particular, is not to establish the nature of the reality, whatever it may be, but to construct the most economic way by which the totality of the observed phenomena, in all their diversity, can be explained.
@Behnam Farid and Marc Monsia. Sure, as it is hegemonically taught, the copenhaguist QM is not more a science at all : it is a mathematical phenomenology, it agglomerates incompatible scales, and condenses and freezes several professional faults.
Waves of probabilities do not exist at all in the real world.
"Collapse" does no exist. But it is taught.
The QMechanists believe in the macro-time of the laboratory, and believe they may extrapolate it at quantic scale. But the reality lashes out in the shafts.
Real individual waves exist, but as individual, they have one emitter and one absorber.
So is the physics of the real world. Some hate it...
And it has already appreciable results.
Article Fifteen surreptitious, copenhaguist and corpuscularist postu...
Neurology is much more a natural science : each case is unique, and we must documentate it very thoroughly. Only small and partial animal experiments.
In clinical psychology, we had to elaborate new tools, to keep a firm grip on reality. One of these is the reflexive tools on back-transfer : What does the patient make me feel ? Why do I have this feeling in reaction to his/her feelings and behavior ?
It is not yet truly scientific, but it tends in the direction.
Again in clinical psychology, I have discovered a rule that can not be refuted in the Popper's meaning : the overt paranoia comes when one is terrified of risking to be unmasked. This statement has been proved powerful, predicting right. BUT... Where to find a someone who asserts and proves : "Yes I am paranoiac, but no, I have nothing shameful to hide !" ? So the epistemologic status of my statement remains delicate.
Milton Erickson had this discipline to get more scientific in his pronostics : he sealed an envelope with his pronostic for this patient or for this family, put it in the drawer, and opened it only years later, when he saw what had been the evolution.
When they respect deontology, psychotherapists use supervision by a senior therapist. Alas in France medicine doctors who are psychiatrist never do... Their feeling of omniscience and impunity... Jacques Antoine Malarewicz has written "Supervision en thérapie sysémique ; le thérapeute familial et son superviseur". ESF éditeur.
Of course I know mock-therapists who are mere murderers :