Either history does NOT EXACTLY repeat or the future is too unpredictable to risk such rationalism. https://www.researchgate.net/publication/377663987_Respectfully_and_Unfortunately_The_Improbability_of_and_Danger_in_Believing_in_Reincarnation
Although comparing the rise and fall of empires there are always similarities, the specific events (wars, climate change, development of new technologies, etc) are never exactly the same. Many ancient civilizations arose in fertile regions that later became barren, or were cut off from imports from other regions that had been crucial to maintaining their status. In other cases, as is happening all over the world today, too much power has been put in the hands of too few, causing discontent that undermines the economy, and leads to international or civil wars that destroy or impoverish the countries involved. And it is almost certain that the end of OUR civilization will be the complete annihilation of all life on Earth, so at least THAT historical episode will not mimic any other one on OUR planet, thought it might be the most common end for a multitude of now-extinct ALIEN civilizations.
History is both subjective (as a humanistic endeavor of narrowly specialized academics) and an objective evolution in the world (which can be understood somewhat as a complex chaotic evolution near "fixed points" on Poincare projections). Therefore, I would expect a human historian to emphasize "historical recurrence" as experts, whereas one will observe a certain "fixed point" behavior, partly dependent on the dimensionality of the Poincare map and boundary effects. Topologically, a bigger picture would suggest that even "attractive" fixed points on a 2D map will not persist: Maps, unfortunately, are not totally capturing the reality, which is likely to be either higher dimensional or reflective of behaviors we cannot measure or account for. But observable map trends might be useful for "rough predictions".
I recall Nietzsche's eternal recurrence theory (https://en.wikipedia.org/wiki/Eternal_return). However, he did not know current cosmological ideas, which are contrary to it.
There is a scientific form of eternal recurrence, formulated by Poincare (who has already being mentioned in this discussion): https://en.wikipedia.org/wiki/Poincar%C3%A9_recurrence_theorem
As other physical laws for closed systems, its apllication to open systems or to the full universe is doubtful.