Astronomers don't "believe" the sun will come up tomorrow. They have certain degree of expectation based on probability, which is based on observed phenomena, knowledge of the solar system, knowledge of the age of the Sun, the longevity of similar yellow stars, etc. In other words it's based on the law of averages, a purely mathematical construct.
Whether or not that will work in the future is a "thing unseen" requiring faith
Not really, annalex. Astrophysicists can tell you pretty much that the Sun will undergo some significant changes at one point in its life, turning into a red giant and engulfing the inner planets, including the earth. If the sun behaves like hexatrillions of other stars, the probability is high that the earth will disappear before the sun does. But at one point, the sun should use up its nuclear fuel and turn into a carbon star, that will burn itself into iron, and collapse onto itself and explode, becoming a very dense white dwarf that will spin at incredible speed until it burns out and becomes space debris and "dark matter."
Can there be exceptions? Sure. The probability exists even for that. In other words, scientists don't "hope" to be right on things unseen in the future; they place a certain degree of probability on an event based on the laws of nature and observed phenomena.
The point it, whether the scientific model is stochastic or any other kind, the faith is that the model that worked in the past will work in the future. Once that is posited axiomatically, sure you can make predictions as per the model.