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"based on the assumptions" is a correct and usable phrase in written English.
You can use it when you are referring to something that is determined or evaluated assuming certain circumstances are true or accepted. For example, "Based on the assumptions that the economy will improve and interest rates will remain low, I have decided to make a substantial investment."
Exact(60)
"Based on the assumptions you have entered, your retirement assets will run out in 2027," it warned.
The model is based on the assumptions of an ideal incompressible fluid and relative rotational motion.
can only provide a score based on the assumptions that are given to them," Mr. Boehner said.
HFA is generally based on the assumptions of homogeneity, independence and stationarity of the hydrological data.
Growth is forecast at 1.8% in 2016 and 1.1% in 2017, based on the assumptions of smooth post-Brexit negotiations and a limited increase in economic barriers".
The formulation is based on the assumptions of Timoshenko beam theory and the nonlinear von-Karman strain displacement relationships.
Based on the assumptions of Euler Bernoulli beam theory, the equations of motion account for small strains but large rotations.
Both models are based on the assumptions of rigid blocks and mortar joints modelled as elastic interfaces.
The formulation is based on the assumptions of the first order shear deformation theory for thin, shallow shells.
The analysis is theoretical and based on the assumptions of total reflux/reboil ratios and infinite number of stages.
(Note: the study was based on the assumptions of the Energy Department's 2010 annual energy outlook, which appeared before the recent downturn in vehicle miles traveled became clear).
More suggestions(18)
based on the premises
based on the projections
imposed on the assumptions
based on the conjectures
based on the hypothesis
based on the inequalities
based on the numbers
based on the facts
based on the works
based on the outlines
based on the parents
based on the tips
based on the songs
based on the lives
based on the notions
based on the beliefs
based on the opinions
based on the supposition
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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