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The phrase "a satisfactory model of" is correct and usable in written English.
You can use it when discussing a representation or framework that meets certain criteria or expectations in a specific context, such as scientific, academic, or theoretical discussions.
Example: "The researchers developed a satisfactory model of climate change that accurately predicts future trends."
Alternatives: "an acceptable representation of" or "a suitable framework for".
Exact(8)
Although living organisms are composed of cells, actual genomic and proteomic data have not yet led to a satisfactory model of working cell in silico.
For example, it was observed that very complex curves were required to produce a satisfactory model of BMC versus age in the entire population, due to the exponential BMC accrual observed in younger subjects combined with a consolidation phase of BMC in early adulthood and then a relatively modest decline in BMC that occurs during aging.
This experimental protocol may provide a satisfactory model of sarcoidosis.
A satisfactory model of navigation should be able to predict behavioral responses to various stimulus waveforms.
This type of analysis, combining molecular data with "typical" morphological characteristics, has sometimes failed to yield a satisfactory model of character evolution [ 24].
It is difficult to build a satisfactory model of the transmission of infectious diseases due to deficiencies in both theory and data [ 14].
Similar(52)
This leads to a satisfactory modeling of the test results.
A satisfactory modeling of the spectra can be obtained if four Gaussians are used.
Essential and up-to-date theoretical, numerical and experimental methodologies are covered, as a tool to progress towards a satisfactory modeling of the nonlinear behavior of structures.
It is shown how, on the basis of certain assumptions, a monopole or in-line dipole source serves as a satisfactory model for the acoustic behaviour of a moving vehicle.
The PBIAS values − 4.6 and 3.8 are within PBIAS < |25%|, can be said to describe a satisfactory model performance for monthly data of the stream flow (Dourte 2011; Moriasi et al. 2007).
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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