Is it obligatory to perform ghusl every time semen is discharged, even if one does not recall a wet dream, knowing that this occurs twice a week?

If you wake up and find wetness, if you are certain it is manī (seminal fluid), then ghusl (definition) (ritual bath) is obligatory. If you are certain it is not manī, then ghusl is not required, but wash whatever it has touched. If you are unsure whether it is manī or not: if you recall having a wet dream, then it is manī and ghusl is obligatory. If you did not see anything in your dream, and your sleep was preceded by thoughts of intercourse, then it is madhī (pre-seminal fluid). If it was not preceded by such thoughts, the correct view is that ghusl is not obligatory, based on the principle of presumption of innocence (bara'at adh-dhimma). The smell of wet manī is like dough or the spathe of a date palm, and when dry, like egg white. Ghusl is obligatory every time you have a wet dream. There is no need to worry, as this is a natural occurrence.