I have been researching this forever and feel like I am so close, but not quite there. Sadly, we only see Frank's shoes in a single scene in Donnie Darko (in two shots) and it is very dark.
I feel absolutely confident in the following:
Beyond that, everything is a guess.
Here is the best reference I have from the BluRay.

The closest semi-match I have been able to find has been the Adidas Brougham Run-DMC and the Adidas Forum.
Adidas Brougham
(Issues: Black strip at bottom of tongue, black on bottom of sole)

Adidas Forum
(Issue: blue on bottom of sole)

I feel ;ike I am SO close, but just not quite there. If I can't find any other options, I will go with the Adidas Forum, but I would REALLY like to hear from anyone who knows a bit more about shoes that might help me nail down those last details so we can once and for all put this issue to rest.
I feel absolutely confident in the following:
- Frank's shoes are Adidas (as are many in the film)
- They are primarily white leather.
- They have an all-white rubber sole.
- Just above the sole, on the back half of the shoe is a dark stripe that has a wave at the top of it.
- The "Adidas" trademark three stipes are dark in color.
Beyond that, everything is a guess.
Here is the best reference I have from the BluRay.

The closest semi-match I have been able to find has been the Adidas Brougham Run-DMC and the Adidas Forum.
Adidas Brougham
(Issues: Black strip at bottom of tongue, black on bottom of sole)

Adidas Forum
(Issue: blue on bottom of sole)

I feel ;ike I am SO close, but just not quite there. If I can't find any other options, I will go with the Adidas Forum, but I would REALLY like to hear from anyone who knows a bit more about shoes that might help me nail down those last details so we can once and for all put this issue to rest.