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Compatible.
Neurobiology is the science that studies the patterns of the nervous system and nervous activity. Therefore, compatibility is expressed in the answer to the question about the functioning of “free will” within the nervous system.
It is studied, as far as I know, by two main routes. The first is the neurophysiology of an elementary volitional act. As in Libet's classic experiment, when a person at some indefinite moment decides to move his hand, and “free will” is a nervous activity from the beginning of making a spontaneous decision to the beginning of its motor execution.
The second is the internal representation of probability theory. Here, neurobiological “free will” is the neural activity associated with calculating the consequences of making a decision based on an internal statistical forecast.
For more information, see the Wikipedia articles “Neuroscience of free will”and ” Neuroeconomics”.
This is a very difficult question, and I've thought about it a lot myself.
First, we can formulate this question even more generally: is the case compatible with our universe? After all, there are clear laws of physics (even if not fully known to mankind), and everything turns out this way and only in the way it can turn out. However, there is such a thing as quantum uncertainty, which spoils this picture of the predictability of the future. If it were not for her, it would be safe to say that absolutely everything is predetermined.
Second, let's first understand what “free will” is. There are many opinions on this subject, but let's assume that free will is precisely the theoretical ability to determine a person's actions and consider this issue exclusively from the point of view of neuroscience. We will refer to action as nerve impulses received from the brain in response to nerve impulses and hormones received in the brain. In this case, two absolutely identical brains (sets of interconnected neurons) will respond exactly the same way to the same nerve impulses and hormones received in the brain, and will change in the same way. That is, from the point of view of neuroscience, there is no freedom of choice in this particular formulation of this concept.