Yes there is! The tiles are almost certainly porcelain. They are designed to grip the dirt and by their very nature they don't let go of it easily. Apply Faber Disycott, scrub it in with a Rotary Scrubber Fitted with a soft to medium brush then if necessary add some 220 Grit Honing Powder and scrub again. Extract with a wet vac, then rinse with a pH Neutral Cleaner and extract again. I would then seal the tiles to make it easier to clean next time.
Kev