Are "intelligent" systems able to bypass the uncertainty principle? This paper talks about finding theoretical correlations to experiential phenomena in quantum mechanical experiments using artificial intelligence (AI).
If AI applications can be sufficiently well trained in theoretical simulations using Schrödinger's equation, is it possible to actually use it to predict position-momentum and the like to arbitrary levels of accuracy by virtue of some (yet unknown) pattern, thereby being able to possibly describe deterministic relationships between non-commuting variables?
I am interested in knowing the possible limitations/lack of it, of an intelligent system in such tricky areas like the foundations of quantum mechanics.
Edit: Now that I have read comments and answers like this, I am also interested to know about efforts to actually find problems with the uncertainty principle, using methods of computation like in the mentioned answer.
 A: tl;dr– Yes, a physicist might come up with a model that supersedes those with an uncertainty-principle, and such a physicist might be an AI.

This is a pretty simple topic overall.  In short:

*

*A better model of reality could find the uncertainty-principle to be emergent, dispensing with it in favor of describing what it emerges from.


*The better model could be found by a sufficient intelligence, be it human, AI, or otherwise.


*So, yes, an AI could potentially dispense with the uncertainty-principle.
That said, the linked paper discusses simulated systems:

Machine learning models are a powerful theoretical tool for analyzing data from quantum simulators, in which results of experiments are sets of snapshots of many-body states.

A god-like AI with infinite computation could, in principle, find the ultimate truth of anything it analyzes.  So if it analyzes real experimental data, then it could find deeper models of physics.
But, if it's looking at simulated data, then the ultimate truth that it'd find would be an exact description of the simulation – not necessarily what the simulation was attempting to emulate.  And if the simulation respects something like an uncertainty-principle, then a perfect analysis of it would reflect that.
Likewise, a god-like AI analyzing a simulation of Newtonian physics wouldn't discover quantum-mechanics nor relativity.  But the AI could discover quantum-mechanics and relativity from looking at real data, even if the folks who made the AI thought the world was perfectly Newtonian.
A: An intelligent system just learns from the data. But the data forbids such violations, so no AI, unless is failing, would predict such a violation of the uncertainty principle.
A: Now that's a nice question. I've only browsed the paper you submitted, so correct me if I misinterpreted it. But the idea there is to use machine learning methods to identify those features of a collection of quantum data that are best suited to be used as characteristic features to the processes at play there. So this is about analyzing data. Therefore, simply put, as long as the data doesn't violate the uncertainty principle, neither will the AI the paper talks about.
But I think your question is a bit more ambitious. Any AI that is trained on a data set can in principle be asked to make predictions about data it has not yet seen, and your question is what it is that hinders the AI to make arbitrarily accurate predictions, thus giving both the momentum and the position of a particle to arbitrary degrees of accuracy. Now, this is much more about physics than it is about AI.
I think the key aspect here is to ask what it means to know a particle's position and momentum. We don't have to go to AI there, we can for example look at something as simple as the ground state of a particle in a 1D box. We consider this problem in classical Schrödinger QM (which, as commenters correctly pointed out, is only a fraction of all of QM). This state can be described by the wave function
$$\psi_1(x,t) = e^{-i\omega_1 t} \cos\left(\frac{\pi}{L}x\right),$$
for $x \in (-L/2,L/2)$, where $L$ is the size of the box and $\omega_1 = \pi^2\hbar/2mL^2$. This is, for all we know by the Schrödinger picture of quantum mechanics, the exact state the particle is in. I repeat that: This is everything we can know about the state of a particle in a box, when someon gives us this wave function, we solved the problem of finding the particle's ground state.
A naive way to look at this wave function is to go to use Born's rule to find the probability distribution (which happens to be stationary because we chose an eigenstate of the Hamiltonian $H$)
$$\rho(x) = |\psi(x,t)|^2 = \cos^2\left(\frac{\pi}{L}x\right)$$
and argue that the particle it describes just wiggles around between $-L/2$ and $L/2$ with this given probability, and once we measure position, we pick up the particle's position at an instant, losing momentum information. But this is just one way of looking at it, and it is problematic, albeit there are ways to make it mathematically sound. This picture leads to a confusion, namely that you think that there is something like the particle's position that is independent of measurement. And at the same time, there is something like the particle's velocity that is independent of measurement, it's just measurement that necessarily discards some of that information, but one could try to get a smart AI to track them both.
But this is not really the data you have. The wave function - encapsulating the full knowledge of the state of the particle - contains no information about the particle's exact position or momentum at an instant. The history of QM showed that it is hopeless to try to maintain our intuition about what position and momentum is. Yes, you can get well-defined relations between them for each path in a path integral formalism, but then you suddenly find the particle tracing out multiple paths. Or you add global hidden variables (like e.g. Bohmian mechanics) to recover a well-defined concept of position and momentum, but then those are not measurable so they come back to haunt you whenever you perform a measurement. There really isn't a way around this: A clear concept of position and momentum can not be maintained at the quantum level. The AI cannot be "smarter" or "more observant" than the maximum information available, which is encoded in the wave function. The information you desire to trace with your AI does just not exist in the way you would need it to.
If you are interested, there is a nice 3Blue1Brown video about the mathematical origins of uncertainty in Fourier analysis which also talks about another aspect of this question, even beyond the scope of quantum physics. I can recommend that.
