The opposite of forget is "remember".
Forget is a compound verb, formed with the preposition for and the verb get. Its inflection broadly follows get, and is therefore an irregular verb; it has a 3rd person form "forgets", the 3rd person form "forgetting" (with a double T), an irregular preterite "forgot", and an irregular past participle "forgotten". The pattern follows the American inflection of get (get+got+gotten) rather than the British inflection (get+got+got).
"Forget+to-infinitive" is semantically different to "forget+gerund", e.g. "I forgot to lock my house" (CCQ: Did I lock my house? No.) v. "I forget locking my house" (CCQ: Did I lock my house? Yes). This difference is also found in remember.
Instead of a gerund, it may be better to use a relative clause, e.g. "I forgot that I had locked my house".