Same thing happened wit Duckweed in my little Koi spa/pond after several deluges of rain. I setup a screened outflow (overflow) to try to curtail the plants from exiting the pool. That worked until the screen was blocked by floating plants, meanwhile the rain kept on coming. In the Winter I cover the spa with sliding glass door glass.
I have other immersed plants growing in the Koi pond such as Hornwart
Hornwart which is a free floating nonvasular (no root) plant that makes buckets full of biomass for compost. Also I've had good luck with Water Lettuce
Pistia
Both stay in the pond just fine no matter how much rain we get.
Halloween-snow-2018-kio-pond-hugelkultur-stabilizer
Brian