There's certain non-filled places in the IPA chart because we physically can't pronounce them. For example, a velar trill or glottal trill.
Using computers, is it possible that we could simulate how these sounds would sound? Has this already been done?
Good question!
For vowels, the chart actually shows a continuous space, with height, backness, and rounding corresponding to values we can measure (and synthesize): the formant positions.
For consonants, the chart isn't actually a perfect representation of how the mouth works. Some things, like the place of articulation of plosives and fricatives, are actually continuous: a human can make a palatal fricative, or an alveolar fricative, or a fricative anywhere in between, for example. And a computer can do the same.
But other things on the chart aren't continuous in the same way. Trills, for example, can only exist at certain places of articulation, because only certain parts of the mouth are flexible enough to trill. And there's not really anything acoustic in common between them, except that they're trill-like: there's not some clean measurable value that's highest for bilabial trills, in the middle for alveolar trills, and lowest for uvular trills, for instance. If there were, we could interpolate between the alveolar and uvular to make a velar trill, but unfortunately there's not.
Similarly, clicks at different places of articulation involve entirely different processes, so there's no way to "fill in the gaps" and figure out what impossible clicks (like the velar click) would sound like.
Other sounds are considered "impossible" because they're exactly the same as other sounds. For instance, a glottal trill is marked impossible. That's not because there can't be any vibration down in that part of the larynx, but because there's already a name for when the vocal folds vibrate and nothing else is articulated: we call it [ə] (in other words, the most central, mid, neutral vowel).
Now, there are some impossible sounds we can create using computers! For example, we can simulate a vowel that's higher and further to the front than [i], which is as high and front as the human mouth can go. Or we can go lower than [a], or farther back than [u], or any combination of these. I'm not sure if anyone's ever researched how people would perceive these impossible sounds: if they'd sound unnatural and unlike any other vowel, or if they'd just be perceived as [i], [a], [u]. That would be an interesting experiment to run.
I think it is not possible to accurately model the acoustics of the impossible sounds. The greyed-out impossible cells are cases judged to be incompatible with human physiology (as opposed to the clear blank cells which are "not attested"). In the case of existing sounds, we can observe their actual articulatory state and derive a tube model where you can compute the resonance and airflow properties of the sound in question. If the articulatory state is impossible, it's hard to model that state and derive an acoustic output.
The case of the impossible labiodental and bilabial laterals is fairly obvious, in that "lateral" pertains to air flow over the (raised) tongue and labiodentals and bilabials don't raise the tongue. This likewise covers glottal laterals. Trills require aerodynamic vibration which depends on having a low-mass articulator in a narrow (high-velocity) stream of air. A uvular trill is possible because the uvula is not very massive, but the tongue body is quite massive and can't be made to "trill". ("Glottal trilling", however, is very common – that's essentially what voicing is, so there we have a different name for that physiological state). In the case of a pharyngeal nasal, it's not that the articulatory state can't be formed, it's that nasalization would have no acoustic consequences.
That's not to say that we can't make up some sound that has a relation to the imagined articulation (except in the case of a meaningless articulation like "labio-lateral"), so we could form a ballpark idea. Here is an example that's in the same county as the ballpark containing a velar trill. Some of the simply unfilled but possible cells don't even need fancy computer modeling, you can just record a labiodental stop, though it could be a challenge to leard to distinguish it from a bilabial stop. Some of the gaps are simply attestation gaps, such as the retroflex lateral fricative. The bilabial trill [ʙ] wasn't added to the IPA until there was a successful campaign showing that it has phonemic status in a couple of languages. I think the case of the uvular tap is like that: it is a sound in a number of languages near the Niger delta, but it has not been shown to be irresolutely phonemic. The sound can be symbolically approximated as [ɢ̆].
Vowels, however, are a continuum: they don't have cells, they have neighborhoods.
