If “the mind” in your question means a non-material entity that exists in an animal and that can sense signals from the environment (see, hear, smell, etc.), operate the signals, resulting in various mental activities (thinking, solving problem, planning, remembering, recalling, etc.), and send signals to its effectors (hand, legs, lips, etc.) to respond to the environment, then the answer is yes. There is a physical theory (with scientific evidence and verifiable predictions) that proves that there is no need to presuppose the existence of something like a luminiferous ether or any other exotic entity to explain the mind and its existence – the mind is just the information-processing processes of the brain. The theory that proves this is “The Basic Theory of the Mind”.
This theory also proves that qualia (i.e., what the color red is like, what the happiness is like, what the thinking is like, etc.) and consciousness (i.e., the awareness and experiences of what the color red is like, of what the happiness is like, of what the thinking is like, etc.) are also physical phenomena that need no exotic entities to account for – they are just signaling patterns and signaling states of neural processes.
Other interesting concepts of this theory are as follows:
Because a neural process that performs a certain function without qualia occurring and a neural process that performs the same function with qualia occurring have different information in the processes, they require different signaling patterns. Therefore, they have different physical effects on other neural processes, at least from the different effects of different signaling patterns. Qualia thus have physical effects.
In addition, because qualia induce the consciousness neural process to create conscious awareness and experiences of themselves and because the consciousness neural process is a physical process, qualia cause changes in a physical process and thus have physical effects.
It can be proved similarly that consciousness (conscious awareness and experiences) has physical effects.
The fact that qualia and conscious awareness and experiences of them occur in only the final-stage sensory perception and the highest-level cognitive and executive neural processes, which are the latest-evolved neural processes, and never occur in more primitive neural processes, such as the brainstem, cerebellum, and basal ganglia, indicates that they are results of nervous system evolution.
The fact that it took more than two billion years after life had appeared on earth and hundreds of millions of years after the nervous system had developed before neural processes that were advanced enough to create qualia and consciousness could emerge into existence also means that qualia and consciousness came into existence because of no other cause than evolution.
The fact that qualia and consciousness still exist today indicates that they have been selected to remain in the evolutionary process. This means that they must have effects that help increase the chance of survival of animals that have them. Qualia and consciousness thus are the evolved functions to help increase the chance of survival of animals, including humans, that have them.
Thus, it concludes that we (our minds with qualia and consciousness) are evolved physical entities to help increase the chance of survival of ourselves and our species and that you (your mind with qualia and consciousness) are here to help increase the chance of your own survival and your species.
There are several other theories about consciousness and qualia but none directly answer your questions about the mind as this theory does. I list some of them here in case you are interested in reading more about this matter:
Block N. Comparing the major theories of consciousness. In: Gazzaniga MS, editor. The Cognitive Neurosciences (Chap 77). 4th ed., Cambridge, MA: MIT Press; 2009:1111–1122.
Kanai R, Tsuchiya N. Qualia. Current Biology. 2012 May;22(10):392–396.
Orpwood R. Neurobiological mechanisms underlying qualia. J Integr Neurosci. 2007 Dec;6(4):523-540.
Seager W. Theories of consciousness. An introduction and assessment. 2nd ed. New York, NY: Routledge; 2016. ISBN 978-0-415-83409-4.