Is the main reason why chaotic systems are so difficult to analyse

>>9097275
i dont think so because you need all the data, all the input causes to do that and you dont have it.

but look up variational bayesian methods. geoff hintons late 80s/early 90s papers on EM, autoencoders and free energy minimisation.

also tomasso poggios regularization.

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>>9097275
If you can reasonably know most of the important parameters of the system you might be able to make somewhat accurate predictions with computational methods rather than mathematical ones. ABM, perhaps

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No. Number of variables doesn't much matter, there are multivariable systems we can predict well and single variable systems that are chaotic.
Chaotic systems are fully deterministic so in principle you can use them to make accurate predictions but they are characterized by exponentially fast divergence of initially infinitesimally close trajectories, ie small changes in initial conditions very quickly make a huge difference.
Even if you had a complete multivariable model and unlimited computing power the weather is chaotic. The model's predictions from temperature=30 would be completely different to temperature=30.000001 after a few days. That's why weather forecasting sucks.
>one day suddenly was some breakthrough
To be useful for predictions the breakthrough would have to be in data measurement. But as the time the predictions are accurate for increases linearly the required data precision increases exponentially so there's not much hope for future 100 day accurate weather forecasts anyway.

Wouldn't the uncertainty principle prove that we'll never have enough information to go off of to predict chaotic systems.

>>9097340
Depends on the scale of the system. Quantum effects are not always important. Chaotic systems are unpredictable because mathematically solving such problems has been close to impossible. You can always march through such systems with numerical analysis, but the cost is always prohibitive.

>>9097340
If the system depends on information governed by the uncertainty principle yes there'd be a fundamental limit on how good your data could be and that translates to a limit on how long a prediction would remain accurate for.

>>9097340
The number of particles involved in an air parcel would cause any probabilities to reliably regress to the mean