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The phrase "approach reported in" is correct and usable in written English.
It can be used when referring to a specific method or strategy that has been documented or discussed in a particular source, such as a research paper or article.
Example: "The approach reported in the recent study offers new insights into the problem."
Alternatives: "method described in" or "strategy outlined in".
Exact(43)
The approach reported in this work is to combine the plasma immersion ion implantation technique with conventional physical vapour deposition.
The suspended DNA bundles were prepared with a well-established approach reported in previous papers24,25,26 (see the Methods section).
The chemisorption approach reported in the present paper appears to be applicable to all kinds of proteins.
The approach reported in this work could be useful for controllable heteroatoms co-doping of other types of new generation graphitic carbon materials.
To validate the developed modeling scheme and the parallel approach reported in the literature, the experimental observations for hydrogenation of alpha-methylstyrene to cumene have been employed.
The approach reported in this work would be potentially important for developing more efficient catalysts for biomass conversion in the future.
Similar(17)
However, the approaches reported in past publications are inherently flawed.
Most model-based diagnosis approaches reported in the literature adopt a generic architecture and approach.
The results indicate that the proposed approach outperforms the other approaches reported in the literature.
The derivations are based on the established approaches reported in the literature with different boundary conditions.
Significant improvement in both static and dynamic performances could be observed, compared to many existing approaches reported in the literature.
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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