Q. how to rid my garden of morning glories (which is very invasive)?
Ipomoea nil, commonly know as morning glory, can become an aggressive plant in a garden.
Yes, a charming vine can self seed too easily, and can be invasive in some states. It's best to pull the seedlings as soon as seen if not desired.
The species plants have escaped gardens and naturalized throughout much of the U.S. In a garden they can self seed a lot! Once self-seeded in a garden it can really take off. Morning glories are aggressive plants, if you don't remove them when small, they will grow vigorously to climb over shrubs, and other plants in your garden.
And if you notice the vines returning in Spring without you having had to plant fresh seed, be vigilant! Look for stragglers outside your property, and pull them up or spray them with white vinegar or other non-chemical herbicide on a dry day. Because at your house they're probably among the best flowers you can grow. Next door, they're weeds. Note: please don't use toxic chemicals to control weedy plants.
Note: There are white varieties of cultivated morning glory that are as annual in nature as their more familiar blue and purple flowered cousins. But if you didn't PLANT white morning glories and white flowers appear on morning glory-like vines, destroy every last one: That's bindweed, a noxious perennial that loves to strangle other plants.
Hope this helps.