What? This is a tree forum.

Then when I go to your post, it looks like you've already identified them ....

I know what the caterpillars are. I would like to know what kind of trees they are on.

I know what the caterpillars are. I would like to know what kind of trees they are on.

Oh, so you did say that! :)

It's hard to see, but for the imperial moth, I did find this information about the host plants:

Conifers and deciduous trees and shrubs including pine (Pinus), oak (Quercus), box elder (Acer negundo), maples (Acer), sweet gum (Liquidambar styraciflua), and sassafras (Sassafras albidum).

But I don't think that leaf looks like any of those ~

The Polyphemus moth appears to be on an alder, but since the resource I found says this: "oak (Quercus), willow (Salix), maple (Acer), and birch (Betula)." then I would say it is probably on a birch as the leaves are very similar.

Those white dots on the main leader suggest birch, but I agree that it look more like an alder. After all birch and alder are in the same family so I guess an alder might do for a hungry caterpillar if there are no birches around.

It is Betula nigra, river birch.

Looks more like an alder to me. FWIW, red alders are common (even weed) trees in this area and Polyphemus moth larvae love them.