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The phrase "are actually based on" is correct and usable in written English.
You can use it when discussing the foundation or origin of something, indicating that it is grounded in certain principles, facts, or ideas.
Example: "The theories presented in the paper are actually based on extensive research conducted over several years."
Alternatives: "are fundamentally derived from" or "are rooted in".
Exact(27)
However, the major reinforcement learning-based theoretical models of classical conditioning (crudely, prediction learning) are actually based on rules designed to explain instrumental conditioning (action learning).
And Van Klaveren and his entire team are actually based on Salford Quays.
There are filmmakers who work very hard to produce films that are actually "based on real events": they are called documentarians.
To the Editor: Ben Greenman's essay "True Lies" registers his indignation with literary works that claim to be fiction but are actually based on writers' experiences.
The identities of Dupont's subjects appear generic — post-human Everymen — but the sculptures are actually based on a three-dimensional scan of the artist's body, executed in 2004 at General Dynamics.
But that is not quite right either: though printed the same size as the paintings they mimic, Ms. Core's photographs are actually based on photographic reproductions found in books and catalogs.
Similar(33)
The shade Sheer Apricot is actually based on one of my favorite, discontinued lip colors.
The story was actually based on one of Altman's dreams, hence the trance-like quality and minimal plotlines.
The DRG-based costliness CMI, which is actually based on charges instead of costs, is used in Medicare's Prospective Payment System[ 4].
The medical program in one of the schools that was involved in the study is actually based on an Australian medical program.
Sadly, this scene was actually based on a real incident.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com