Are there any methods to predict the location of a jet aircraft from its sound?
From a single spotting location, then yes by training. But for any location, then it's very hard. Our ears get confused when the sound reflects off the surrounding surfaces, e.g., ground, buildings, etc. And when the sound comes from above.

Most mammals are adept at resolving the location of a sound source using interaural time differences and interaural level differences. However, no such time or level differences exist for sounds originating along the circumference of circular conical slices, where the cone's axis lies along the line between the two ears.
Consequently, sound waves originating at any point along a given circumference slant height will have ambiguous perceptual coordinates. That is to say, the listener will be incapable of determining whether the sound originated from the back, front, top, bottom or anywhere else along the circumference at the base of a cone at any given distance from the ear.

Tilting your head might help though.
So much so, airplane spotters in WWII judging only by sound misjudged the direction of Allied bombers and the entire Luftwaffe was sent looking in the wrong direction, only to realize the direction reported was incorrect and they had to land once they started running out of fuel.

Göring freely admitted the laugh was on him, that he had sent the Luftwaffe on a mammoth tour of their own air space.

But with computers it can be done using 3D sound localization. Or good old locators:
(theatlantic.com) Chinese soldiers man a sound detector which directs the firing of 3-inch anti-aircraft guns, around the city of Chongqing, China, on May 2, 1941.
P.S. Same problem arises when trying to figure out where an artillery fire is coming from or going to.