Cohomology of Deligne-Lusztig varieties for short-length regular elements in exceptional groups

We determine the cohomology of Deligne-Lusztig varieties associated with some short-length regular elements for split groups of type F4 and En. As a byproduct, we obtain conjectural Brauer trees for the principal Φ14-block of E7 and the principal Φ24-block of E8.