Location of the Frigidus River

[Robert Vermaat]

As for the plumbata, that road ran through the Julian Limes and I would guess that there were many battles and skirmishes fought there.
Do you know if any of those finds (plumbata) were dated to late 4th, early 5th centuries?

Most if not all, those that can be dated. But indeed, it's a very strategic route, which was taken by almost any invasion force wanting to invade Italy or Illyria/Pannonia.

About the valley from Castrum to Ad Pirum, a river runs through there. If that were the battle's location, I wonder why it wasn't called the battle of Bela River?

Bela seems like a Slavic name to me (meaning 'white')?

There is also a comment by at least one historian that Alaric led Roman forces down a narrow valley with archers on both sides (Aiding in the Defense). I don't see such a narrow defile between Castrum and Ad Pirum.

I do. Both routes have narrow defiles, but I agree that such a descrition would fit better with a battle at the southern end of the Vipava valley. Nevertheless, this was quite a large battle, and parts of it could have taken place miles apart. And since both routes meet south of Ajdovščina/Castra, I think it remains possible, whichever of the 2 routes favoured, that a main battle took place on the banks of the Vipava river, south of Ajdovščina/Castra. I would not bet on any remains, because rivers like these often burst their banks and change course across the whole valley floor.