This is insultingly bad from a physics and logic point of view. That system cannot exist. The physics explanation is hard(er) but the logical one is easy. Let's even ignore you'd have to input every atom and particle with precise characteristics at Planck precision at the same time. Suppose you could. Still an easy defeat: make a machine that makes world-altering decisions (market trades, company promotions etc.) based on the brightness of an oscillating star. Can the system predict it, as "deterministic" as it may be, without even having the input data? (i.e. every molecule of that star's system) (please note there is no spoiler here - no twist revealed, nothing on characters etc.)

This lack of logic translates further into the show, in the characters' decisions etc. but I'll let you find that out on your own.