Answer: Outside of a willow or alder, I can't think of a single tree that will put up with wet soils. Both these trees can get quite large, but both will provide summer shade.
Alocasia esculenta, or Elephant's Ear, is a wonderfully lush, tropical looking plant that tolerates wet soils. It grows about 5' tall and 4' across, bearing 2' long leaves so it won't provide much shade.
Instead of a tree or shrub, you might consider installing a trellis and growing a vining plant such as Akebia, Ivy, or Kiwi. These plants are tolerant of varying soil conditions and will provide summer shade.
Best wishes with your landscape!
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