Get some 30 second cleaner, actual name and a power scrubber brush, spray it on, rinse really good and let dry. I've used it on my Sunbrella cushions

I always used dish soap and stiff scrub brush on mine.

While the power wash left lines, it was pretty effective. If worst comes to worst, I'd do a lot of it in hopes that you can reduce the lines eventually.

Is that mildew rather than just dirt?
For several years I have sprayed my cheap chair cushions with Clorox Clean up, let them soak for a while and then rinsed thoroughly.