If you’re looking at design alternatives, start with the culvert inlet. Wingwalls and a headwall would get more flow into the culvert. Another remedy would be to upsize the culvert. Whatever is going on at that constriction will affect how the bed adjust to stream flows.
If you’re asking about changing the modeled bed to reduce modeled overtopping, it is possible to design a transition that minimizes head loss at the inlet. But that is design for concrete form work that might be applied to a low loss aqueduct ($$), not natural bed and bank materials.