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The phrase "principles underlying" is correct and can be used in written English.
It is typically used when talking about fundamental truths that form the basis of something, such as a moral or scientific principle. For example: "The principles underlying quantum mechanics are particularly complex and difficult to understand."
Exact(60)
Principles underlying calculations of stellar structure.
Here are five basic principles underlying the technology.
The naïve utility calculus: Computational principles underlying commonsense psychology.
Recognize the general principles underlying common statistical procedures.
They discover the principles underlying the centrifuge, the invention on which nuclear energy relies.
"They were hand-picked because of their specific interest in the cognitive principles underlying the magic".
It also reviews principles underlying the design of biopolymer.
Here we analyse principles underlying the dynamics and statistics of power grid frequency fluctuations.
Yacob, J. et al. Principles underlying chromatophore addition during maturation in the European cuttlefish, Sepia officinalis.
This article describes some simple games, discusses different theories, and outlines principles underlying game theory.
Ting, L. H. et al. Neuromechanical Principles Underlying Movement Modularity and Their Implications for Rehabilitation.
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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