NASA is describing that they are predicting the eclipses based on the ancient Saros Cycle as used by the Ancient Babylonians.
No, they are not claiming to use the Saros Cycle to predict eclipses. They talk about how the geometry of the earth-moon-sun system creates the cycle, but not how to use the cycle to predict eclipses. For example, they say that a cycle moves from partial eclipses to total eclipses "after ten or eleven Saros cycles..." Well, which is it this Saros, ten or eleven? How would you know? In fact, if you look on
another of their pages you find the situation is more unpredictable than that: "the number of partial eclipses in the initial phase ranges from 6 to 25" with no guidance on how to know from past cycles how many might be in future cycles. The futility of using the Saros cycle for prediction is made fully evident when they sum it all up: "...the exact duration and number of eclipses in a complete Saros is not constant. A series may last 1226 to 1550 years and is comprised of 69 to 87 eclipses, of which about 40 to 60 are central" That's no kind of basis for prediction!
Everything in astronomy is predicted on basis of patterns.
No, it is not. Patterns are a starting point. Understanding the reason for the patterns and (just as important) the deviations from those patterns yields better tools for prediction. For example, each Saros cycle has a different number of eclipses in it, and a different number of partial, annular, hybrid (sometimes zero), and total (sometimes zero) eclipses. How can that form the basis for prediction? The interval between eclipses in the same Saros is eight years, eleven days, and approximately eight hours. APPROXIMATELY. How can THAT form the basis for prediction? The answer is that it cannot, and it does not. The Saros Cycle is a way to categorize eclipses. To predict them you need to know the underlying physical movements, not just look up dates in a chart and project forward from them.