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Mathematics disproves Matrix theory, says reality isn’t simulation
(interestingengineering.com)
This is a most excellent place for technology news and articles.
The amount of computer power used to run those simulations is immense, and even then, the predictive capacity of those models starts degrading rapidly around 7 to 10 days ahead. There's some amazing science that goes into those models, but the results are hard-won. And what we know about more energetic systems (say, the magnetohydrodynamics of the sun) is far less comprehensive.
And be careful with that "fundamentally chaotic" assertion: there are degrees of how chaotic a system is, and some aspects of a system can be more deterministic than others.