dominant = having power and influence over others
"Predominant" has two meanings:
1. having control or power over others;
2. being present as the strongest and main element.
So in a sentence such as "White is the predominant colour of his bedroom", it is definition 2, and we cannot use "dominant" instead.
In a sentence such as "The Socialists are the predominant party in the National Assembly", we can use "dominant" instead and keep the meaning unchanged.