There's two related problems here: finding relevant results and ranking those results. The first is historically done with massive inverted indexes. Page rank is for the second one of ranking those relevant results.
For the first part you can look into "embeddings" and "approximate nearest neighbor lookup" for the modern approaches. That said inverted indexes are still very popular.
The second one is generally called "learning to rank" so you can find a lot of things written on that topic. The biggest issue here imho is what training data you use which gives you examples of good rankings. The best algorithm trained on garbage will give you garbage.
Comments
There's two related problems here: finding relevant results and ranking those results. The first is historically done with massive inverted indexes. Page rank is for the second one of ranking those relevant results.
For the first part you can look into "embeddings" and "approximate nearest neighbor lookup" for the modern approaches. That said inverted indexes are still very popular.
The second one is generally called "learning to rank" so you can find a lot of things written on that topic. The biggest issue here imho is what training data you use which gives you examples of good rankings. The best algorithm trained on garbage will give you garbage.