Are there specific supplications that Allah (SWT) taught His Messenger (PBUH) to invoke?

The established prophetic supplications are a revelation from Allah, as He states: ﴿Nor does he speak of (his own) desire. It is only a Revelation revealed.﴾ [An-Najm/3-4]. We are commanded to follow the Prophet (peace and blessings be upon him) in his sayings and actions, as Allah says: ﴿There has certainly been for you in the Messenger of Allah an excellent pattern for anyone whose hope is in Allah and the Last Day and [who often] remembers Allah.﴾ [Al-Ahzab/21]. All established prophetic supplications possess this characteristic.